Dynamical quantum simulations as laboratories for quantum information

Brian Barch; Greeshma Oruganti; Hailey S. Murray; Luis Pedro Garc\'ia-Pintos; Mark M. Wilde; Martin Larocca; M. Cerezo; Su Yeon Chang

REVIEW

Dynamical quantum simulations as laboratories for quantum information

Su Yeon Chang, Hailey S. Murray, Brian Barch, Greeshma Oruganti, Luis Pedro García-Pintos, Martin Larocca, Mark M. Wilde, M. Cerezo

Quantum Physics · Submitted 27 Oct 2026 · 65 references

Pith's verdict: Solid analytic core with real capacity identities; the readout-reversal claim is plausible but needs a sensitivity analysis before the numerics carry the headline.

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CitationBrian Barch, Greeshma Oruganti, Hailey S. Murray, Luis Pedro Garc\'ia-Pintos, Mark M. Wilde, Martin Larocca, M. Cerezo, Su Yeon Chang. "Dynamical quantum simulations as laboratories for quantum information." arXiv:2610.37589 (2026). https://pith.science/paper/VUJA7WCV

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Editor's note

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Two things to know. The analytic core in Supplemental S15 is the real payload: exact Bell-state recovery fidelity, quantum capacity Q = 1 − chi of the complementary region, classical capacity equal to the Holevo information, and the Bell-pair distillation rate — all proved from standard theorems under stated assumptions, including a genuinely optimal recovery operation with a trace-norm-duality converse, degradability, and a spin-flip-symmetry reduction of the input optimization. I checked the logic of those derivations; they hold. The authors are also unusually careful about scope: they repeatedly spell out when an identity is a coding statement rather than a single-copy claim, and when Gaussian reconstruction agrees at the scalar level but fails at the operator level. That care is earned.

The one place to push before buying the headline is the XX/XXX readout reversal. The stress-test concern is fair: matching is performed on the same budget that appears in the denominator of the compared ratios (eta_Delta matched on Delta, eta_chi matched on chi, eta_F matched on log F_Q), one configuration, no sensitivity analysis over floors, calipers, or the rank-versus-raw rule. But it is not fatal. The raw width-seven medians in Table I show the same ordering with no matching at all, and the commuting-readout restriction in S8 reproduces the reversal under a different procedure. The angle-estimation claim is the softest spot: there the raw representative trajectory favors XX, so the matched QFI comparison carries the entire weight. A referee should ask for sensitivity analysis across the matching choices, for the bond-dimension and truncation-error data that S1 asserts without reporting, and for code and data. For a paper whose numerics were AI-assisted and unreleased, the reproducibility burden is higher, not lower.

One minor item: the multipartite Rains definition is imported from a self-cited preprint [51]. The paper's certification is independently corroborated by max-Rains and log-GMN, which are grounded elsewhere, so I would treat this as minor.

Who this is for: people running local-pulse response simulations on quantum hardware, who get a map of what else their prepared states contain, and the spin-chain-as-channel community, who will want the F_Bell and Q = 1 − chi identities. It deserves a serious referee — the analytic core justifies referee time even if the numerical comparison needs strengthening.

Referee report

Significance

The analytic core is a genuine strength: the Bell-recovery formula with its converse, the capacity identities, and the distillation-rate identity in S15 are derived from stated theorems (Uhlmann, Fuchs–van de Graaf, Devetak–Shor, Holevo–Schumacher–Westmoreland, Devetak–Winter), and no fitted parameter enters any capacity or fidelity derivation. The spin-flip reduction to the maximally mixed input and the degradability argument are verified and correctly qualified, including the p-optimized formula (S58) for the case without symmetry. The identities Q(N_{R,t})=1−χ_Ē(t) and F_Bell≥1−Δ_K/2 are falsifiable and give the earlier trace-distance and Holevo plots a second, quantum-capacity interpretation. The numerical study is extensive and internally consistent: the quadratic Δ→χ scaling with the Pinsker coefficient is verified, the Gaussian-surrogate limitations are stated honestly (Sec. V.A, Fig. 7), and the raw-versus-matched distinction is acknowledged (Sec. V.B, Sec. VI). If the matched-comparison robustness is established, the representation–readout reversal is a significant and counterintuitive result for reusing response-protocol simulations.

Major objections (2)

[§V.B, Table I, Eqs. (58)–(61); §VI, Eq. (69), Fig. 9(c); Supplemental S14] The matched XX–XXX comparison is the controlled evidence behind the headline reversed ordering, and as reported it does not exclude a selection artifact. Each readout fraction has the matching variable in its denominator (η^{prodP}_Δ = Δ_prod/Δ, η^{χ,prodP} = I_prod/χ, η^{prodP}_F = F_C^{prodP}/F_Q; Eqs. (58)–(61) and (69)), and the material floors (Δ ≥ 0.05, χ ≥ 0.05; S14) confine the comparison to the high-budget regime. The finite-pulse matching is performed on the pooled empirical rank of the budget with a caliper of 0.10 in rank, not on the raw budget (S14). Because the XX and XXX budget distributions differ (median Δ7 = 0.2936 vs 0.2300 and χ7 = 0.1087 vs 0.0618, Sec. III.A), rank-matched pairs can carry raw-budget differences of the order of the inter-model median gap, which is the same order as the reported fraction differences (0.6050 vs 0.6604 in Table I); a systematic within-pair budget imbalance would bias the XXX-minus-XX differences positive even at equal absolute readout. The Fisher comparison is better controlled (raw log10 FQ with a 0.05-decade caliper), but the allowed within-pair FQ ratio of about 1.12 is still non-negligible relative to the effect. Only one configuration is reported: the bootstrap intervals cover time-block resampling and rematching, but not the choice of floors, calipers, or rank-versus-raw matching, and the raw comparison in Fig. 9(b) shows the opposite ordering, so the matched procedure carries the full weight of the persistence claim in Sec. VI. I note that the raw medians in Table I and the larger raw budgets in XX are consistent with the claimed direction; the problem is that the quantitative control intended to establish the claim at comparable budgets is currently unvalidated. Please report: (i) within-pair balance on the raw budgets per stratum; (ii) sensitivity of the matched differences to floor values (e.g., 0.02/0.05/0.10), caliper widths (0.05/0.10/0.20), and raw-budget versus rank matching; (iii) the numbers of matched and unmatched observations per aperture and stratum; and (iv) numerical values of the matched differences with confidence intervals for each stratum, rather than the single statement that all differences are positive. The same single-threshold structure recurs in the I3 analysis (Sec. IV.C, χ_AB ≥ 0.05), which would also benefit from a threshold sensitivity check.
[Supplemental S1] The numerical convergence statement is asserted but not evidenced. S1 reports that representative evolutions were repeated at increasing maximum bond dimension and that "the observables and reduced density matrices used in the analysis were unchanged within the numerical accuracy of the calculation," but no bond dimensions, truncation errors, discarded weights, or convergence curves are reported anywhere. The width-seven late-time reduced states that feed Table I and Figs. 2–8 are exactly the objects least protected by an unquantified check, and the effect sizes at stake in the readout fractions are of order 0.05 in the fraction. Please report the maximum bond dimensions used (as a function of time for each model), the truncation error or discarded weight, and a direct check that the readout fractions and the matched XXX-minus-XX differences are stable under bond-dimension increase.

Minor objections (5)

[General (notation)] The proliferation of readout metrics (η^{1P}_Δ, η^{prodP}_Δ, η^{χ,prodP}, η^{prodP}_F, c_off, g_coh, I3, and the matched-difference statistics) makes the main text dense; a summary table or glossary of definitions with equation numbers would materially improve readability.
[§III.A and §V.B] The quoted medians (e.g., the Δ7 medians 0.2936/0.2300 and all Table I fractions) are taken over the "resolved" wake defined by activity masks that are specified only in S14; restating the masks and the numbers of surviving observations in the main text would make these numbers auditable.
[§VIII.C, Eqs. (93)–(100)] The inequality chain R ≤ R_max ≤ E_GMEN is quoted from Refs. [50,51], and Ref. [51] is an arXiv preprint rather than a published proceedings or journal article. Since the certification claim in Fig. 12 relies on this chain, a one-sentence derivation of the second inequality, or a statement of the publication status of [51], would make the section self-contained.
[§VII.C and passim] Numerous typographical slips remain, e.g., "auxilary" in §VII.C; a careful proofreading pass is needed.
[Fig. 5(a,b)] The caption reports the fitting range (10^{-5} ≤ Δ ≤ 0.05) but not the number of data points or the fit quality; a sentence with the number of observations per fit would strengthen the claimed verification of the quadratic scaling.

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The paper

The paper claims

The states behind a Green-function simulation carry a full quantum-information record, and this paper shows how to read it.

The reading

This paper argues that a quantum simulation built to compute one quantity — here, the spin Green function of a finite XX or XXX chain through opposite local pulses — necessarily prepares a family of many-body states that can be interrogated for far more than that single response. Reading the pulse sign as an encoded classical bit, the authors follow how the resulting 'source record' propagates, how it is encoded across local subsystems, and how much of it different measurements can recover. The central finding is a separation between representation and readout: in the free-fermion XX chain, fermionic covariance data exactly reconstruct the signed response $\xi$, yet simple product-Pauli spin measurements recover a larger fraction of the available record in the interacting XXX chain (width-seven decision fractions $0.6050$ versus $0.6604$). The reversed ordering persists when the task changes from discriminating two finite pulses to estimating a continuous source angle at matched quantum Fisher information, and the same reduced states yield exact Bell-state recovery fidelities, quantum and classical communication rates, and direct certification of genuine multipartite entanglement.

What carries the argument

The load-bearing objects are the two local branch states $\rho_\pm = \bar\rho \pm \xi$, where $\bar\rho$ is the sign-forgotten average state and $\xi$ is the Hermitian, traceless 'signed response' that carries all dependence on the pulse sign; from them the trace distance $\Delta_R = \|\xi\|_1$ fixes the optimal single-copy decision probability and the Holevo information $\chi_R = S(\bar\rho) - [S(\rho_+) + S(\rho_-)]/2$ sets the measurement-independent information budget of the observation region. The local-pulse protocol $V_s = \exp(-is\pi P/4)$ with opposite signs supplies the encoded classical bit, and the $U(1)$ magnetization symmetry together with global spin-flip symmetry fix the one-site common-basis structure and later make the maximally mixed input optimal for the capacity identities. For the representation–readout separation, the machinery is the Majorana covariance matrix $\Gamma_{ab}$ of a fermionic Gaussian state, which is an exact description of the XX dynamics and is used to build a Gaussian surrogate of the XXX states whose operator-level error grows with aperture while its scalar quantities remain close. For the quantum-information recovery, the machinery is the controlled encoding $C_V$ that turns a superposition of pulse signs into a quantum channel; degradability of that channel plus spin-flip symmetry yields the exact identities $Q(\mathcal{N}) = 1 - \chi_{\bar{R}}$ and $C(\mathcal{M}) = \chi_R$.

Extended reading notes

Core claim

On the paper's own terms, the claim is that a standard dynamical simulation is already a quantum-information experiment: the reduced states $\rho_+$ and $\rho_-$ created by opposite pulse signs carry a source record whose accessibility depends on the task, the spatial aperture, and the measurement family. Concretely, it claims a clear separation between representation and readout: in the XX chain the Jordan–Wigner covariance matrix is an exact description of the state and exactly determines the signed response $\xi = (\rho_+ - \rho_-)/2$, whereas in the XXX chain that covariance reconstruction degrades as the aperture grows (median normalized signed-response error near $0.70$ at width seven), even though the reconstructed trace distance and Holevo information stay close to their physical values. Nevertheless, restricted spin measurements recover a larger fraction of the locally available record in XXX at matched signal strength, and the reversal also holds for estimating a continuously varying source angle when observations are matched in local quantum Fisher information. The same reduced states support exact quantum-information identities — an optimal single-copy Bell-state recovery fidelity $(1 + \sqrt{F(\rho_+,\rho_-)})/2$, coherent information $1 - \chi_{\bar{R}}$, quantum capacity $Q(\mathcal{N}) = 1 - \chi_{\bar{R}}$, and classical capacity $C(\mathcal{M}) = \chi_R$ — and certify that five-site blocks remain genuinely five-partite entangled over most of the dynamics while a propagating perturbation reorganizes entanglement across spatial scales.

Load-bearing premise

The load-bearing premise is that the matched XX–XXX comparisons are unbiased: observations are filtered by activity floors ($\Delta \ge 0.05$ or $\chi \ge 0.05$) and paired by deterministic bipartite matching with calipers of $0.10$ in rank and $0.05$ decades in log Fisher information, and if those masks or the pairing rule favor regions where XXX readout is efficient, the reversed ordering would be an artifact of the comparison procedure rather than a property of the models; the matrix-product-state convergence behind all of the data is also asserted without reported bond dimensions or truncation errors.

Editorial extensions

If this is right

Existing response simulations can be re-analyzed without new time evolution: the already-computed trace-distance and Holevo wakes $(\Delta_K, \chi_K)$ double as bounds on Bell-state recovery and, through $\chi_K \mapsto 1 - \chi_K$, as exact quantum-capacity maps for the complementary region.
Experiment design should optimize the physical measurement family rather than the compact representation: the free-fermion XX chain admits an exact covariance description, yet a smaller fraction of its source record is accessible to spin-Pauli readouts than in the interacting XXX chain.
Five-site reduced states of a standard spin-chain simulation certify genuine five-partite entanglement over most of the dynamics (median Rains entanglement $0.0164$ in XX and $0.0329$ in XXX), complementing indirect QFI-based entanglement-depth estimates from the dynamical structure factor.
The identities $Q(\mathcal{N}) = 1 - \chi_{\bar{R}}$ and $C(\mathcal{M}) = \chi_R$ mean that measuring one region's Holevo information determines both the achievable classical communication rate to that region and the qubit-transmission capacity of its complement, with one-site losses quadratic in the retarded Green function.
The propagating perturbation reorganizes entanglement across spatial scales: the observed block typically becomes more entangled with its exterior while bipartite and genuine multipartite entanglement inside the block decrease, and forgetting the pulse sign hides additional internal entanglement, substantially more in XX.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

I would expect the representation–readout gap to be a recurring pattern in integrable models whose quasiparticle description differs from the measured degrees of freedom; a direct test is to apply the paper's matched-comparison machinery to an XX chain with a small integrability-breaking perturbation and watch whether the Pauli-readout fractions shift as the Gaussian structure is lost.
The capacity identity suggests a practical diagnostic for spin-chain quantum communication: estimating the Holevo information of a block through randomized measurements immediately bounds how many qubits per use can be transmitted through the complementary region, without running any communication protocol.
The strongly negative tripartite flank information in XX despite separable flank states indicates that the joint encoding is likely kinematic — a property of free-fermion mode structure and shared classical correlations — rather than entanglement-based; a covariance-only computation of $I_3$ would settle this.
The reversal claim is only as strong as the matching protocol, so I would stress-test it by repeating the matched comparison on the unmasked grid with alternative pairing rules; if the XXX-minus-XX differences stay positive in every stratum, I would take the reversal to be a property of the models rather than of the selection.

Original abstract

Dynamical quantum simulations are commonly designed to access a particular response function or correlation function. Yet the underlying protocol prepares a family of many-body states that contains information well beyond the observable for which the simulation was originally designed. In this work, we explore the idea of using these states as laboratories for quantum information. As a case study, we consider the local-pulse protocols used to compute Green functions in finite XX and XXX spin chains, and we interpret opposite source rotations as encoding a classical bit into the many-body system. This allows us to follow how the resulting record propagates, how it is encoded across local subsystems, and how readily it can be accessed with different measurements. We also find a clear separation between representation and readout. While fermionic covariance data exactly reconstruct the signed response in the XX chain, simple spin measurements recover a larger fraction of the locally available information in the XXX chain. This reversed ordering persists when we move from finite-pulse discrimination to local source-angle estimation. Going beyond the source record, the same reduced states also allow us to reinterpret results in terms of Bell state recovery and quantum communication rates, as well as providing direct access to the evolving bipartite and genuine multipartite entanglement of the system. Our results show that dynamical quantum simulations developed for response calculations can naturally be used to ask a much broader set of quantum-information questions about the many-body states they already prepare.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-28: 1 request, 7,525 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.51 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Dynamical quantum simulations are commonly designed to access a particular response function or correlation function. Yet the underlying protocol prepares a family of many-body states that contains information well beyond the observable for which the simulation was originally designed. In this work, we explore the idea of using these states as laboratories for quantum information. As a case study, we consider the local-pulse protocols used to compute Green functions in finite XX and XXX spin chains, and we interpret opposite source rotations as encoding a classical bit into the many-body system. This allows us to follow how the resulting record propagates, how it is encoded across local subsystems, and how readily it can be accessed with different measurements. We also find a clear separation between representation and readout. While fermionic covariance data exactly reconstruct the signed response in the XX chain, simple spin measurements recover a larger fraction of the locally available information in the XXX chain. This reversed ordering persists when we move from finite-pulse discrimination to local source-angle estimation. Going beyond the source record, the same reduced states also allow us to reinterpret results in terms of Bell state recovery and quantum communication rates, as well as providing direct access to the evolving bipartite and genuine multipartite entanglement of the system. Our results show that dynamical quantum simulations developed for response calculations can naturally be used to ask a much broader set of quantum-information questions about the many-body states they already prepare.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Dynamical quantum simulations are commonly designed to access a particular response function or correlation function.	background 1.00	0.05	0.02	asserted 1.00
s1	Yet the underlying protocol prepares a family of many-body states that contains information well beyond the observable for which the simulation was originally designed.	gap 0.59	0.12	0.09	asserted 1.00
s2	In this work, we explore the idea of using these states as laboratories for quantum information.	contribution 1.00	0.33	0.09	asserted 0.61
s3	As a case study, we consider the local-pulse protocols used to compute Green functions in finite XX and XXX spin chains, and we interpret opposite source rotations as encoding a classical bit into the many-body system.	method 0.67	0.79	0.04	asserted 0.96
s4	This allows us to follow how the resulting record propagates, how it is encoded across local subsystems, and how readily it can be accessed with different measurements.	method 0.55	0.77	0.04	asserted 0.91
s5	We also find a clear separation between representation and readout.	result 0.85	0.87	0.08	asserted 1.00
s6	While fermionic covariance data exactly reconstruct the signed response in the XX chain, simple spin measurements recover a larger fraction of the locally available information in the XXX chain.	result 1.00	0.95	0.07	asserted 1.00
s7	This reversed ordering persists when we move from finite-pulse discrimination to local source-angle estimation.	result 0.99	0.90	0.06	asserted 1.00
s8	Going beyond the source record, the same reduced states also allow us to reinterpret results in terms of Bell state recovery and quantum communication rates, as well as providing direct access to the evolving bipartite and genuine multipartite entanglement of the system.	result 0.47	0.92	0.11	asserted 0.94
s9	Our results show that dynamical quantum simulations developed for response calculations can naturally be used to ask a much broader set of quantum-information questions about the many-body states they already prepare.	interpretation 0.92	0.82	0.93	asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.82 · evidence from simulation or computation 0.95.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Schematic representation of our framework. A dynamical quantum simulation prepares a family of rich many-body states as the system evolves. In the conventional view, these states are used to estimate a target dynamical quantity, such as a response function or spectrum that can be compared with experiment. Here we instead take the prepared states themselves as objects of study and use them to investigate quantum-information properties such as information propagation, encoding and readout, and entanglement structure. Motivated by this question, here we propose to view dynamical…

**Figure 2.** Trace distance wakes for all observation apertures. Trace distance maps for XX (a-d) and XXX (e-h) at widths k = 1, 3, 5, 7. Every panel uses the same absolute scale. At fixed time and center, the regions are nested, so enlarging the aperture cannot reduce the distinguishability. The maps locate the record over the space-time window. We next ask how much information about the source label s is present in the qubits within the region R. The Holevo information of the local ensemble quantifies this information and is defined as χR := S(¯ρ) − S(ρ+) + S(ρ−) 2 (16) where S(ρ) is the von

**Figure 3.** Trace distance at the source as a function of time for the four observation apertures k = 1, 3, 5, 7. Solid (dashed) lines correspond to the XX (XXX) chain, with colors indicating the aperture size. For k = 1, the trace distance is directly related to the conventional local retarded response through ∆1(t) = 2|G R zz(j0, j0;t)|. Increasing the aperture reveals a substantially larger and longer-lived record of the same perturbation. The more persistent oscillatory structure in XXX follows that of the quantum-wake behavior of the isotropic Heisenberg chain. This aperture dependence is…

**Figure 4.** Holevo-information wakes for all observation apertures. The layout and absolute spatial and temporal scales are the same as in

**Figure 5.** Weak-signal scaling and aperture dependence of the trace distance and Holevo information. Panels (a) and (b) show XR as a function of ∆2 R for the XX and XXX chains, respectively, restricted to 10−5 ≤ ∆R ≤ 0.05. Colors denote the aperture width k, and solid lines show independent power-law fits XR ∝ (∆2 R) m. The fitted exponents remain close to m = 1 for every model and aperture, confirming the quadratic scaling XR ∝ ∆2 R when the two local branches are nearly indistinguishable. Panels (c) and (d) show the median ∆R and XR, respectively, as a function of k, with shaded regions

**Figure 6.** From a common-basis one-site record to joint multisite encoding. (a) The optimized one-qubit projective information equals the one-site Holevo information. (b) The off-diagonal weight coff of ξ in the eigenbasis of ρ¯ becomes nonzero on wider blocks. (c) Median ∆comm/∆ with 5th to 95th percentile ranges. Less of the XX decision bias survives the commuting restriction. (d) For the nonlocal width-seven geometry A|center|B, the classical source-label tripartite information is negative across the nonlocal region shown. This additional symmetry is what fixes the one-site average state…

**Figure 7.** Gaussian reconstruction of the XXX source record at the operator and scalar levels. (a) Median normalized signed-response error e ξ G as a function of the aperture k, with shaded regions showing the 5th–95th percentile range. The covariance reconstruction becomes progressively less accurate at the operator level as the aperture grows. (b) Ratios of the Gaussian and physical trace distances, ∆G/D, and Holevo informations, χ G/χ. The horizontal line marks exact agreement. Despite the growing operator-level error in panel (a), both scalar quantities remain close to their physical…

**Figure 8.** Restricted spin measurements recover a larger fraction of the source record in XXX. (a) Width-seven median accessibility for the best single Pauli string, η ∆ 1P, and for product-Pauli measurements optimized for binary decision, η ∆ prodP, or source-label mutual information, η χ prodP. All three fractions are larger in XXX. (b) XXX-minus-XX differences after comparing observations with similar available information. Decision readouts are matched at comparable trace distance ∆, while the information readout is matched at comparable χ. The comparison is performed separately for each…

**Figure 9.** Source-angle sensitivity and its accessibility under product-Pauli readout. (a) Quantum Fisher information FQ(θ) for representative width-five source-region states as the pulse angle is varied. (b) Corresponding fraction η F prodP = F prodP C /FQ accessible to optimized product-Pauli measurements. For this representative trajectory, η F prodP is generally larger in XX, while the two models also have substantially different FQ. (c) Matched XXX-minus-XX differences in η F prodP for widths three and five in source and nonlocal regions, after comparing observations with similar local…

**Figure 10.** The source record as an obstruction to quantum recovery. (a) One share of a Bell state coherently selects the pulse sign. The many-body evolution acts only on RR¯. The receiver retains the control A and the region R, applies an arbitrary joint decoding channel, and seeks a Bell state between the output B and the untouched reference A ′ . The two lower input wires are prepared jointly in |gϵ⟩; they need not be in a product state. The block CV denotes both nontrivial pulses in Eq. (70). (b) The arrow changes the interpretation of the plotted region. An existing plot for a region K…

**Figure 11.** Entanglement between and within the observed block changes across the propagating wake. Width-seven branch-averaged changes relative to the physical t = 0 post-pulse state in the block–exterior entanglement entropy ∆SR for (a) XX and (b) XXX, and in the median logarithmic negativity across internal contiguous bipartitions, ∆EN,med, for (c) XX and (d) XXX. Positive ∆SR indicates increased entanglement between the observed block and the rest of the chain, while negative ∆EN,med indicates a reduction of entanglement across typical cuts within the block. Each quantity uses a symmetric…

**Figure 12.** Genuine five-partite entanglement in the local reduced states. Width-five multipartite Rains entanglement R for (a) XX and (b) XXX, max-Rains entanglement Rmax for (c) XX and (d) XXX, and genuine multipartite log-negativity E GME N for (e) XX and (f) XXX. Positive values of each quantity certify that the five-spin reduced state is not biseparable. For each measure, the XX and XXX panels use the same color scale, allowing the magnitude and space-time structure to be compared directly between the two models. convex mixture of states that are separable across possibly different…

**Figure 13.** Change in genuine multipartite Rains entanglement versus block–exterior entropy. Change in the Rains entanglement ∆R versus the change in block entropy ∆SR for the same reduced states in the XX and XXX models. Most observations have ∆SR > 0 and ∆R < 0, showing that increased entanglement between the block and its exterior typically accompanies a reduction of genuine multipartite entanglement within the block. The distinct branches traced by XX and XXX show that this reorganization differs between the two dynamics. The genuine multipartite entanglement follows the same overall…

Figures reproduced from arXiv:2610.37589 by the authors.

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E. Granet, K. Murota, H. Dreyer, K. Yamamoto, J. Pedersen, and H. Suwa, Dynamical structure fac- tor with a pumping approach on a trapped-ion quantum computer, arXiv preprint arXiv:2607.07138 10.48550/arXiv.2607.07138 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2607.07138 2026
[10]

M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. D. Lukin, and E. Demler, Probing real-space and time- resolved correlation functions with many-body ramsey in- terferometry, Physical Review Letters111, 147205 (2013)

View on Pith 2013
[11]

M. L. Baez, M. Goihl, J. Haferkamp, J. Bermejo-Vega, M. Gluza, and J. Eisert, Dynamical structure factors of dynamical quantum simulators, Proceedings of the National Academy of Sciences117, 26123 (2020)

View on Pith 2020
[12]

Y.-T. Lee, B. Pokharel, J. Cohn, A. Schleife, and A. Baner- jee,Digitalquantumsimulationofspintransport,Physical Review Letters136, 050603 (2026)

View on Pith 2026
[13]

V. Giovannetti and R. Fazio, Information-capacity de- scription of spin-chain correlations, Physical Review A—Atomic, Molecular, and Optical Physics71, 032314 (2005)

View on Pith 2005
[14]

D. Rossini, V. Giovannetti, and R. Fazio, Information transfer rates in spin quantum channels, International Journal of Quantum Information5, 439 (2007)

View on Pith 2007
[15]

R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin, M. Rispoli, and M. Greiner, Measuring entanglement entropy in a quantum many-body system, Nature528, 77 (2015)

View on Pith 2015
[16]

T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing rényientanglemententropyviarandomizedmeasurements, Science364, 260 (2019)

View on Pith 2019
[17]

P. Hauke, M. Heyl, L. Tagliacozzo, and P. Zoller, Measur- ing multipartite entanglement through dynamic suscepti- bilities, Nature Physics12, 778 (2016)

View on Pith 2016
[18]

A. Scheie, P. Laurell, A. Samarakoon, B. Lake, S. Nagler, G. Granroth, S. Okamoto, G. Alvarez, and D. Tennant, Witnessing entanglement in quantum magnets using neu- tron scattering, Physical Review B103, 224434 (2021)

View on Pith 2021
[19]

M. M. Wilde,Quantum Information Theory(Cambridge University Press, Cambridge, UK, 2013)

View on Pith 2013
[20]

B. Schumacher and M. D. Westmoreland, Optimal signal ensembles, Physical Review A63, 022308 (2001)

View on Pith 2001
[21]

A. P. Majtey, P. W. Lamberti, and D. P. Prato, Jensen- Shannon divergence as a measure of distinguishability between mixed quantum states, Physical Review A72, 052310 (2005)

View on Pith 2005
[22]

H. Umegaki, Conditional expectation in an operator alge- bra. IV. Entropy and information, Kodai Mathematical Seminar Reports14, 59 (1962)

View on Pith 1962
[23]

Y. Liu, Quantum state testing beyond the polarizing regime and quantum triangular discrimination, Computa- tional Complexity34, 11 (2025), arXiv:2303.01952 [quant- ph]

View on Pith arXiv 2025
[24]

K. M. R. Audenaert, Quantum skew divergence, Journal of Mathematical Physics55, 112202 (2014)

View on Pith 2014
[25]

F. Hiai, M. Ohya, and M. Tsukada, Sufficiency, KMS condition and relative entropy in von Neumann algebras, Pacific Journal of Mathematics96, 99 (1981)

View on Pith 1981
[26]

T. M. Cover and J. A. Thomas,Elements of Information Theory, Vol. 2 (Wiley New York, 1991)

View on Pith 1991
[27]

A. S. Holevo, Bounds for the quantity of information trans- mitted by a quantum communication channel, Problemy Peredachi Informatsii9, 3 (1973)

View on Pith 1973
[28]

S. Bravyi, Lagrangian representation for fermionic linear optics, Quantum Info. Comput.5, 216–238 (2005)

View on Pith 2005
[29]

N. Gigena and R. Rossignoli, Entanglement in fermion systems, Physical Review A92, 042326 (2015)

View on Pith 2015
[30]

N. Gigena and R. Rossignoli, One-body information loss in fermion systems, Physical Review A94, 042315 (2016)

View on Pith 2016
[31]

M. Di Tullio, R. Rossignoli, M. Cerezo, and N. Gigena, Fermionic entanglement in the lipkin model, Physical Review A100, 062104 (2019)

View on Pith 2019
[32]

M. Walter and F. Witteveen, Computable mea- sures of fermionic non-Gaussianity from the co- variance matrix, arXiv preprint arXiv:2607.02242 10.48550/arXiv.2607.02242 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2607.02242 2026
[33]

S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters72, 3439 (1994)

View on Pith 1994
[34]

P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi, Fisher information and multiparticle entanglement, Phys- ical Review A85, 022321 (2012)

View on Pith 2012
[35]

M. G. Paris, Quantum estimation for quantum technology, International Journal of Quantum Information7, 125 (2009)

View on Pith 2009
[36]

A. Sone, M. Cerezo, J. L. Beckey, and P. J. Coles, A gen- eralized measure of quantum Fisher information, Physical Review A104, 062602 (2021)

View on Pith 2021
[37]

P. Hayden, K. Milner, and M. M. Wilde, Two-message quantum interactive proofs and the quantum separability problem, in2013 IEEE Conference on Computational Complexity(IEEE, 2013) pp. 156–167, arXiv:1211.6120 [quant-ph]. 25

View on Pith Pith review arXiv 2013
[38]

A. Uhlmann, The “transition probability” in the state space of a∗-algebra, Reports on Mathematical Physics9, 273 (1976)

View on Pith 1976
[39]

C. A. Fuchs and J. van de Graaf, Cryptographic dis- tinguishability measures for quantum-mechanical states, IEEE Transactions on Information Theory45, 1216 (1999), arXiv:quant-ph/9712042

View on Pith Pith review arXiv 1999
[40]

S. Lloyd, Capacity of the noisy quantum channel, Physical Review A55, 1613 (1997), arXiv:quant-ph/9604015

View on Pith Pith review arXiv 1997
[41]

I. Devetak, The private classical capacity and quantum capacity of a quantum channel, IEEE Transactions on In- formation Theory51, 44 (2005), arXiv:quant-ph/0304127

View on Pith Pith review arXiv 2005
[42]

I. Devetak and P. W. Shor, The capacity of a quantum channel for simultaneous transmission of classical and quantum information, Communications in Mathematical Physics256, 287 (2005), arXiv:quant-ph/0311131

View on Pith Pith review arXiv 2005
[43]

I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences461, 207 (2005), arXiv:quant-ph/0306078

View on Pith Pith review arXiv 2005
[44]

V. Vedral and M. B. Plenio, Entanglement measures and purification procedures, Physical Review A57, 1619 (1998), arXiv:quant-ph/9707035

View on Pith Pith review arXiv 1998
[45]

A. S. Holevo, The capacity of the quantum channel with general signal states, IEEE Transactions on Information Theory44, 269 (1998), arXiv:quant-ph/9611023

View on Pith Pith review arXiv 1998
[46]

B.SchumacherandM.D.Westmoreland,Sendingclassical information via noisy quantum channels, Physical Review A56, 131 (1997)

View on Pith 1997
[47]

P. W. Shor, Additivity of the classical capacity of entanglement-breaking quantum channels, Journal of Mathematical Physics43, 4334 (2002), arXiv:quant- ph/0201149

View on Pith 2002
[48]

G. Vidal and R. F. Werner, Computable measure of en- tanglement, Physical Review A65, 032314 (2002)

View on Pith 2002
[49]

M. B. Plenio, Logarithmic negativity: a full entanglement monotone that is not convex, Physical Review Letters95, 090503 (2005)

View on Pith 2005
[50]

H. S. Murray, S. Bhattacharya, M. Cerezo, L. Lyu, and M. M. Wilde, Genuine multipartite rains entanglement, in2026 IEEE International Symposium on Information Theory (ISIT)(IEEE, 2026) pp. 1–6

View on Pith 2026
[52]

N. Datta, Min- and max-relative entropies and a new en- tanglement monotone, IEEE Transactions on Information Theory55, 2816–2826 (2009)

View on Pith 2009
[53]

B. Jungnitsch, T. Moroder, and O. Gühne, Taming mul- tiparticle entanglement, Physical Review Letters106, 190502 (2011)

View on Pith 2011
[54]

M. Hofmann, T. Moroder, and O. Gühne, Analytical characterization of the genuine multiparticle negativity, Journal of Physics A: Mathematical and Theoretical47, 155301 (2014)

View on Pith 2014
[55]

H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measure- ments, Nature Physics16, 1050 (2020)

View on Pith 2020
[56]

A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The random- ized measurement toolbox, Nature Reviews Physics5, 9 (2023)

View on Pith 2023
[57]

M. West, A. A. Mele, M. Larocca, and M. Cerezo, Real classical shadows, Journal of Physics A: Mathematical and Theoretical58, 245304 (2025)

View on Pith 2025
[58]

M. West, F. Sauvage, A. Sen, R. Forestano, D. Wierichs, N. Killoran, D. Grinko, M. Cerezo, and M. Larocca, Clas- sical shadows with arbitrary group representations, arXiv preprint arXiv:2604.01429 10.48550/arXiv.2604.01429 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2604.01429 2026
[59]

L. Wang and R. Renner, One-shot classical-quantum ca- pacity and hypothesis testing, Physical Review Letters 108, 200501 (2012)

View on Pith 2012
[60]

F. Hiai and D. Petz, The proper formula for relative entropy and its asymptotics in quantum probability, Com- munications in mathematical physics143, 99 (1991)

View on Pith 1991
[61]

T. Ogawa and H. Nagaoka, Strong converse and stein’s lemma in quantum hypothesis testing, IEEE Transactions on Information Theory46, 2428 (2000)

View on Pith 2000
[62]

M. Fishman, S. White, and E. Stoudenmire, The itensor software library for tensor network calculations, SciPost Physics Codebases , 004 (2022)

View on Pith 2022
[63]

U. Schollwöck, The density-matrix renormalization group, Reviews of modern physics77, 259 (2005)

View on Pith 2005
[64]

A. Lesniewski and M. B. Ruskai, Monotone riemannian metrics and relative entropy on noncommutative proba- bility spaces, Journal of Mathematical Physics40, 5702 (1999). 26 Supplemental Information for Dynamical quantum simulations as laboratories for quantum information The Supplemental Information collects additional results that support the main text. W...

View on Pith 1999
[65]

In particular, it is a positive semidefinite operator with unit trace. It is not the block-diagonal marginalωAR of the Bell-input experiment. TheE marginal of|Υ⟩is(ρ 0,E +ρ 1,E)/2, so purity and the previous identities give FBell(R, t) =1 +∥T R∥12 , I(A ′⟩AR)ω = 1 + S(ρ0,R) +S(ρ 1,R)2 −S(Γ AR).(S74) The second expression is the exact capacity in the spin-...

View on Pith

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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H. S. Murray, S. Bhattacharya, M. Cerezo, L. Lyu, and M. M. Wilde, Flood of multipartite rains entanglement, arXiv preprint arXiv:2608.11406 10.48550/arXiv.2608.11406 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2608.11406 2026

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View on Pith Pith review arXiv doi:10.48550/arxiv.2603.15608 2026

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E. Granet, K. Murota, H. Dreyer, K. Yamamoto, J. Pedersen, and H. Suwa, Dynamical structure fac- tor with a pumping approach on a trapped-ion quantum computer, arXiv preprint arXiv:2607.07138 10.48550/arXiv.2607.07138 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2607.07138 2026

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M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. D. Lukin, and E. Demler, Probing real-space and time- resolved correlation functions with many-body ramsey in- terferometry, Physical Review Letters111, 147205 (2013)

View on Pith 2013

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M. L. Baez, M. Goihl, J. Haferkamp, J. Bermejo-Vega, M. Gluza, and J. Eisert, Dynamical structure factors of dynamical quantum simulators, Proceedings of the National Academy of Sciences117, 26123 (2020)

View on Pith 2020

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Y.-T. Lee, B. Pokharel, J. Cohn, A. Schleife, and A. Baner- jee,Digitalquantumsimulationofspintransport,Physical Review Letters136, 050603 (2026)

View on Pith 2026

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V. Giovannetti and R. Fazio, Information-capacity de- scription of spin-chain correlations, Physical Review A—Atomic, Molecular, and Optical Physics71, 032314 (2005)

View on Pith 2005

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D. Rossini, V. Giovannetti, and R. Fazio, Information transfer rates in spin quantum channels, International Journal of Quantum Information5, 439 (2007)

View on Pith 2007

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R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin, M. Rispoli, and M. Greiner, Measuring entanglement entropy in a quantum many-body system, Nature528, 77 (2015)

View on Pith 2015

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T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing rényientanglemententropyviarandomizedmeasurements, Science364, 260 (2019)

View on Pith 2019

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P. Hauke, M. Heyl, L. Tagliacozzo, and P. Zoller, Measur- ing multipartite entanglement through dynamic suscepti- bilities, Nature Physics12, 778 (2016)

View on Pith 2016

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A. Scheie, P. Laurell, A. Samarakoon, B. Lake, S. Nagler, G. Granroth, S. Okamoto, G. Alvarez, and D. Tennant, Witnessing entanglement in quantum magnets using neu- tron scattering, Physical Review B103, 224434 (2021)

View on Pith 2021

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M. M. Wilde,Quantum Information Theory(Cambridge University Press, Cambridge, UK, 2013)

View on Pith 2013

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B. Schumacher and M. D. Westmoreland, Optimal signal ensembles, Physical Review A63, 022308 (2001)

View on Pith 2001

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A. P. Majtey, P. W. Lamberti, and D. P. Prato, Jensen- Shannon divergence as a measure of distinguishability between mixed quantum states, Physical Review A72, 052310 (2005)

View on Pith 2005

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H. Umegaki, Conditional expectation in an operator alge- bra. IV. Entropy and information, Kodai Mathematical Seminar Reports14, 59 (1962)

View on Pith 1962

[24] [23]

Y. Liu, Quantum state testing beyond the polarizing regime and quantum triangular discrimination, Computa- tional Complexity34, 11 (2025), arXiv:2303.01952 [quant- ph]

View on Pith arXiv 2025

[25] [24]

K. M. R. Audenaert, Quantum skew divergence, Journal of Mathematical Physics55, 112202 (2014)

View on Pith 2014

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F. Hiai, M. Ohya, and M. Tsukada, Sufficiency, KMS condition and relative entropy in von Neumann algebras, Pacific Journal of Mathematics96, 99 (1981)

View on Pith 1981

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T. M. Cover and J. A. Thomas,Elements of Information Theory, Vol. 2 (Wiley New York, 1991)

View on Pith 1991

[28] [27]

A. S. Holevo, Bounds for the quantity of information trans- mitted by a quantum communication channel, Problemy Peredachi Informatsii9, 3 (1973)

View on Pith 1973

[29] [28]

S. Bravyi, Lagrangian representation for fermionic linear optics, Quantum Info. Comput.5, 216–238 (2005)

View on Pith 2005

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N. Gigena and R. Rossignoli, Entanglement in fermion systems, Physical Review A92, 042326 (2015)

View on Pith 2015

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N. Gigena and R. Rossignoli, One-body information loss in fermion systems, Physical Review A94, 042315 (2016)

View on Pith 2016

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M. Di Tullio, R. Rossignoli, M. Cerezo, and N. Gigena, Fermionic entanglement in the lipkin model, Physical Review A100, 062104 (2019)

View on Pith 2019

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M. Walter and F. Witteveen, Computable mea- sures of fermionic non-Gaussianity from the co- variance matrix, arXiv preprint arXiv:2607.02242 10.48550/arXiv.2607.02242 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2607.02242 2026

[34] [33]

S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters72, 3439 (1994)

View on Pith 1994

[35] [34]

P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi, Fisher information and multiparticle entanglement, Phys- ical Review A85, 022321 (2012)

View on Pith 2012

[36] [35]

M. G. Paris, Quantum estimation for quantum technology, International Journal of Quantum Information7, 125 (2009)

View on Pith 2009

[37] [36]

A. Sone, M. Cerezo, J. L. Beckey, and P. J. Coles, A gen- eralized measure of quantum Fisher information, Physical Review A104, 062602 (2021)

View on Pith 2021

[38] [37]

P. Hayden, K. Milner, and M. M. Wilde, Two-message quantum interactive proofs and the quantum separability problem, in2013 IEEE Conference on Computational Complexity(IEEE, 2013) pp. 156–167, arXiv:1211.6120 [quant-ph]. 25

View on Pith Pith review arXiv 2013

[39] [38]

A. Uhlmann, The “transition probability” in the state space of a∗-algebra, Reports on Mathematical Physics9, 273 (1976)

View on Pith 1976

[40] [39]

C. A. Fuchs and J. van de Graaf, Cryptographic dis- tinguishability measures for quantum-mechanical states, IEEE Transactions on Information Theory45, 1216 (1999), arXiv:quant-ph/9712042

View on Pith Pith review arXiv 1999

[41] [40]

S. Lloyd, Capacity of the noisy quantum channel, Physical Review A55, 1613 (1997), arXiv:quant-ph/9604015

View on Pith Pith review arXiv 1997

[42] [41]

I. Devetak, The private classical capacity and quantum capacity of a quantum channel, IEEE Transactions on In- formation Theory51, 44 (2005), arXiv:quant-ph/0304127

View on Pith Pith review arXiv 2005

[43] [42]

I. Devetak and P. W. Shor, The capacity of a quantum channel for simultaneous transmission of classical and quantum information, Communications in Mathematical Physics256, 287 (2005), arXiv:quant-ph/0311131

View on Pith Pith review arXiv 2005

[44] [43]

I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences461, 207 (2005), arXiv:quant-ph/0306078

View on Pith Pith review arXiv 2005

[45] [44]

V. Vedral and M. B. Plenio, Entanglement measures and purification procedures, Physical Review A57, 1619 (1998), arXiv:quant-ph/9707035

View on Pith Pith review arXiv 1998

[46] [45]

A. S. Holevo, The capacity of the quantum channel with general signal states, IEEE Transactions on Information Theory44, 269 (1998), arXiv:quant-ph/9611023

View on Pith Pith review arXiv 1998

[47] [46]

B.SchumacherandM.D.Westmoreland,Sendingclassical information via noisy quantum channels, Physical Review A56, 131 (1997)

View on Pith 1997

[48] [47]

P. W. Shor, Additivity of the classical capacity of entanglement-breaking quantum channels, Journal of Mathematical Physics43, 4334 (2002), arXiv:quant- ph/0201149

View on Pith 2002

[49] [48]

G. Vidal and R. F. Werner, Computable measure of en- tanglement, Physical Review A65, 032314 (2002)

View on Pith 2002

[50] [49]

M. B. Plenio, Logarithmic negativity: a full entanglement monotone that is not convex, Physical Review Letters95, 090503 (2005)

View on Pith 2005

[51] [50]

H. S. Murray, S. Bhattacharya, M. Cerezo, L. Lyu, and M. M. Wilde, Genuine multipartite rains entanglement, in2026 IEEE International Symposium on Information Theory (ISIT)(IEEE, 2026) pp. 1–6

View on Pith 2026

[52] [52]

N. Datta, Min- and max-relative entropies and a new en- tanglement monotone, IEEE Transactions on Information Theory55, 2816–2826 (2009)

View on Pith 2009

[53] [53]

B. Jungnitsch, T. Moroder, and O. Gühne, Taming mul- tiparticle entanglement, Physical Review Letters106, 190502 (2011)

View on Pith 2011

[54] [54]

M. Hofmann, T. Moroder, and O. Gühne, Analytical characterization of the genuine multiparticle negativity, Journal of Physics A: Mathematical and Theoretical47, 155301 (2014)

View on Pith 2014

[55] [55]

H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measure- ments, Nature Physics16, 1050 (2020)

View on Pith 2020

[56] [56]

A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The random- ized measurement toolbox, Nature Reviews Physics5, 9 (2023)

View on Pith 2023

[57] [57]

M. West, A. A. Mele, M. Larocca, and M. Cerezo, Real classical shadows, Journal of Physics A: Mathematical and Theoretical58, 245304 (2025)

View on Pith 2025

[58] [58]

M. West, F. Sauvage, A. Sen, R. Forestano, D. Wierichs, N. Killoran, D. Grinko, M. Cerezo, and M. Larocca, Clas- sical shadows with arbitrary group representations, arXiv preprint arXiv:2604.01429 10.48550/arXiv.2604.01429 (2026)

View on Pith Pith review arXiv doi:10.48550/arxiv.2604.01429 2026

[59] [59]

L. Wang and R. Renner, One-shot classical-quantum ca- pacity and hypothesis testing, Physical Review Letters 108, 200501 (2012)

View on Pith 2012

[60] [60]

F. Hiai and D. Petz, The proper formula for relative entropy and its asymptotics in quantum probability, Com- munications in mathematical physics143, 99 (1991)

View on Pith 1991

[61] [61]

T. Ogawa and H. Nagaoka, Strong converse and stein’s lemma in quantum hypothesis testing, IEEE Transactions on Information Theory46, 2428 (2000)

View on Pith 2000

[62] [62]

M. Fishman, S. White, and E. Stoudenmire, The itensor software library for tensor network calculations, SciPost Physics Codebases , 004 (2022)

View on Pith 2022

[63] [63]

U. Schollwöck, The density-matrix renormalization group, Reviews of modern physics77, 259 (2005)

View on Pith 2005

[64] [64]

A. Lesniewski and M. B. Ruskai, Monotone riemannian metrics and relative entropy on noncommutative proba- bility spaces, Journal of Mathematical Physics40, 5702 (1999). 26 Supplemental Information for Dynamical quantum simulations as laboratories for quantum information The Supplemental Information collects additional results that support the main text. W...

View on Pith 1999

[65] [65]

In particular, it is a positive semidefinite operator with unit trace. It is not the block-diagonal marginalωAR of the Bell-input experiment. TheE marginal of|Υ⟩is(ρ 0,E +ρ 1,E)/2, so purity and the previous identities give FBell(R, t) =1 +∥T R∥12 , I(A ′⟩AR)ω = 1 + S(ρ0,R) +S(ρ 1,R)2 −S(Γ AR).(S74) The second expression is the exact capacity in the spin-...

View on Pith