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REVIEW 3 major objections 4 minor 50 references

Memory effects in repeated uses of quantum channels

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper derives an exact formula for the average fidelity of the n-th use of a quantum state transfer channel when the channel is not reset between uses, and shows that small readout timing errors turn memory effects into severe degradat

desk verdict Useful exact formula for repeated-use QST memory, but the central derivation is omitted and the 'memory always hurts' claim rests on an unproven inequality. read the letter →

arxiv 2511.05661 v1 pith:RIS4DO7R submitted 2025-11-07 quant-ph

Hayden Zammit , Roberto Salazar , Gianluca Valentino , Johann A. Briffa , Tony J. G. Apollaro This is my paper · ORCID
classification quant-ph
keywords memoryeffectsquantumstatetransferrepeatedchannelusespinchainsperfectfree-fermionmodelsMotzkinpathsfidelity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum state transfer is usually analysed under the assumption that the channel is reset after each use. This paper instead treats a channel used repeatedly without resetting, so excitations left in the channel from earlier rounds become a memory that affects later rounds. Its main result is an exact, closed-form expression for the n-th-use Haar-averaged transfer fidelity for any U(1)-symmetric channel mappable to quadratic (free-fermion) models. The expression splits into a term for the current use and a memory factor built from transition amplitudes of previous uses, which for free-fermion systems reduces to amplitudes involving only the sender and receiver sites. Applied to a perfect-state-transfer spin chain with imperfect readout timing, the formula shows that even a 5% timing error lowers fidelity to about 0.91 after ten uses, that longer chains are far more sensitive, and that the second use's quantum capacity is bounded by the first use's. The reason to care: it provides the first general analytical tool for arbitrary reuse counts without resetting, and a practical warning that ubiquitous timing errors turn memory into a severe degradation.

What carries the argument

The memory factor A_{n-1}, computed by summing over Motzkin paths in a rooted tree graph. The graph's nodes are labelled by the number of excitations remaining in the channel (0 at the root, then {0,1} or {n-1,n,n+1} per the generation rule), and edges carry the single-particle transition amplitudes between these excitation-number sectors at each readout time. For quadratic (free-fermion) Hamiltonians, Slater-determinant expansions and the completeness relation eliminate sums over channel sites, so all amplitudes reduce to transitions between the sender site 1 and receiver site N. This reduction is the paper's second main result: the n-th-use fidelity for free-fermion channels depends only o

What would settle it

Take the PST chain of length N=6, choose a non-uniform timing sequence such as t1=0.7τ, t2=1.3τ, t3=0.9τ, and compute the exact n=3 fidelity by full state-vector simulation; compare to eq. (10). Then compute A_2 and A_1 numerically to test whether A_2 ≤ A_1 always holds. A single parameter set where A_2 > A_1, or where eq. (10) disagrees with the exact simulation, would falsify the paper's central claims.

Watch

Extended reading notes

Core claim

The paper's central claim is Eq. (4): for U(1)-symmetric quantum channels whose Hamiltonian maps to a quadratic fermionic model, the average fidelity of the n-th use is ⟨Fn⟩ = 1/2 + |f^N_1(t_n)| A_{n-1}(t_{n-1};...;t_1)/3 + |f^N_1(t_n)|^2/6, where f^N_1(t) is the single-particle transition amplitude between sender and receiver after time t, and A_{n-1} is a memory factor that sums, over all Motzkin paths (sequences of excitation numbers inside the channel after each readout), products of single-particle transition amplitudes. For free-fermion models, the memory factor collapses to combinations of sender–receiver amplitudes, for example B^N_1(t2,t1)=f^N_1(t1+t2)-f^1_1(t1)f^N_1(t2)-f^N_1(t1)f^

Load-bearing premise

The unproven monotonicity inequality 0 ≤ A_{n-1} ≤ A_{n-2} ≤ ... ≤ A_1 ≤ 1 for equal readout timings is the load-bearing premise; if it fails for some parameters, the conclusion that memory effects always degrade fidelity under uniform timing would break down.

Editorial extensions

If this is right

  • For equal readout timings, the memory factor satisfies 0 ≤ A_{n-1} ≤ ... ≤ A_1 ≤ 1, so each additional use lowers the average fidelity unless all previous excitations were fully extracted; this quantifies when resetting is necessary.
  • On a perfect-state-transfer chain, a 5% timing error drops the 10th-use fidelity to about 0.91; with 1% error, chains of ~2000 sites fall below the LOCC limit by the 4th use, showing timing sensitivity grows rapidly with length.
  • For the second use, the channel decomposes into a generalized amplitude-damping channel followed by a dephasing channel, yielding the bound Q(Φ2) ≤ Q(Φ1) under uniform timing; for sufficiently strong damping the capacity vanishes, so entanglement distribution through repeated uses fails in broad time windows.
  • Because the formula applies to any U(1)-symmetric channel mappable to quadratic fermions, it gives a general tool to compare candidate state-transfer protocols for robustness under multiple uses.

Reading between the lines

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

  • The monotonicity of A_{n-1} is asserted as 'evident' without proof; if it fails for some parameters, memory could in principle enhance fidelity for non-uniform timing sequences, so the uniform-timing degradation conclusion is the paper's load-bearing practical claim.
  • The reduction to sender–receiver amplitudes for free fermions suggests that interacting U(1)-symmetric channels, which require the general appendix expression tracking many-particle density elements, might still inherit a Motzkin-path combinatorial structure that could be exploited numerically.
  • The formula's recursive structure hints that A_n might satisfy a closed recurrence in n, which would make predictions for long reuse sequences straightforward without enumerating all Motzkin paths.
  • A natural testable extension is to verify the capacity bound Q(Φ2) numerically for specific chains, and to ask whether the same degradation mechanism bounds higher uses (n>2).
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies repeated uses of a U(1)-symmetric quantum channel for quantum state transfer without resetting the channel between uses. The central result is a claimed exact formula, Eq. (4), for the nth-use Haar-averaged QST fidelity in terms of a single-particle transition amplitude |f_1^N(t_n)| and a memory factor A_{n-1} built from Motzkin-path sums of transition amplitudes. For Hamiltonians that map to quadratic fermionic models, the paper claims the memory factor reduces to amplitudes involving only the sender and receiver sites. The formalism is applied to the Christandl perfect-state-transfer chain with readout timing errors, leading to the qualitative conclusion that memory effects are always detrimental under equal readout intervals. A separate result bounds the quantum capacity of the second-use channel via a decomposition into generalized amplitude damping and dephasing.

Significance. If the central formula is correct, this is a genuinely useful tool: it extends single-use QST fidelity results to arbitrary reuse counts without a reset assumption, and it does so with no fitted parameters. The n=1 limit correctly reduces to the known Bose expression, and the free-fermion reduction to sender-receiver amplitudes is elegant and likely to be widely applicable. The numerical predictions for readout-timing errors, especially the strong sensitivity to chain length, are falsifiable. However, the paper does not actually derive the key equations: Eq. (17) is stated without proof, the reduction to Eq. (4) is not shown, and the monotonicity of the memory factor—on which the 'always detrimental' conclusion rests—is asserted but not proved. These gaps currently prevent verification of the central claims. The capacity bound in Eq. (16) also needs a more careful derivation.

major comments (3)
  1. [Sec. III and Appendix, Eq. (17)] Equation (17) is presented as the general expression from which Eq. (4) is derived, but no derivation is provided. The appendix merely states the formula; the paper does not show the Haar averaging over previous sender states, the U(1) sector decomposition, or how the channel density matrix elements ρ^(n-1) enter. Since Eq. (4) is the central result, the reader cannot check the validity of the averaging or the reduction to A_{n-1}. This is a load-bearing omission and should be fixed by giving the full derivation (or a clear, complete reference if it already exists elsewhere).
  2. [Sec. III, after Eq. (11)] The monotonicity claim '0≤A_{n-1}≤A_{n-2}···≤A_1≤1' for equal readout timings is asserted as 'evident' but is not proved. This is not immediate from the Motzkin-path sum: each path contributes a squared modulus of a sum of complex transition amplitudes, so quantum interference could in principle make A_n non-monotone. The claim is load-bearing because it underpins the paper's main practical conclusion that memory effects are always detrimental under uniform timing. Please provide a proof or, failing that, restrict the conclusion to the cases actually computed and add numerical checks for a range of parameters and chain lengths.
  3. [Sec. IV, Eqs. (13)–(16)] The derivation of the second-use dynamical map Φ2 = ΦGAD ΦPD and the bound Q(Φ2) ≤ p_2 I_c[ΦAD(γ2,0)] + (1−p_2) I_c[ΦAD(γ2,1)] is sketched in one sentence. The bottleneck inequality alone does not directly give this expression, and convexity of the quantum capacity for convex combinations of channels is not generally valid; the argument needs to be written out. In addition, the matrices in Eqs. (14)–(15) are stated without derivation. This part is secondary to the fidelity result, but it is used to support the claim that the second use reduces quantum information transmission, so it should be made rigorous.
minor comments (4)
  1. [Sec. II, Eq. (3)] The notation (t_{n−1}; t_1) is introduced, but the time arguments in Eqs. (2)–(3) are sometimes written with a missing subscript (e.g., 't n−1'); please normalize the typography.
  2. [Sec. III, Eq. (4)] The statement that 'the structure of the nth-use average fidelity is independent of n' would be clearer if qualified: it is independent of n only in the sense that the same functional form with f_1^N(t_n) and A_{n−1} appears; the memory factor itself depends on all previous times.
  3. [Sec. IV, Fig. 4] The figure caption could state whether A_{n−1} was evaluated exactly or by truncating the Motzkin-path sum; for N up to 7500 this is a nontrivial computational point.
  4. [Sec. V and acknowledgements] Several minor typos: 'ACKOWLEDGEMENTS' should be 'ACKNOWLEDGEMENTS', and 'Ackowledgements' in the section heading. Also, the conclusions repeat 'may be inefficient already after the first use', which seems to contradict the title emphasis on repeated uses; consider softening.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the derivation is self-contained and anchored to externally known limits.

full rationale

The central result, Eq. (4), is derived within the paper from unitary evolution, the protocol definitions in Eqs. (1)-(3), Haar averaging over sender states, and the U(1)/quadratic-fermion structure of the channel. No free parameter is fitted to the fidelity predictions: the transition amplitudes f_i^j(t) are computed analytically from the PST Hamiltonian, and the memory factor A_{n-1} is defined as a sum over Motzkin paths rather than being tuned to reproduce the plotted fidelities. The n=1 limit is checked against the externally known Bose result (Ref. [8]), providing an independent anchor. The use of Ref. [23] for Slater-determinant reduction of many-particle transition amplitudes is a standard mathematical tool, not a self-citation that imports the paper's conclusion. The complaint in the skeptic summary concerns the unproven monotonicity assertion 0 <= A_{n-1} <= A_{n-2} ... <= A_1 <= 1 for equal readout timings; this is a gap in proof or a correctness risk, but it is not circularity, because the inequality is not assumed in deriving Eq. (4) nor is Eq. (4) equivalent to it. The derivation therefore does not reduce to its inputs by construction, and no identified step involves fitting data and renaming it a prediction or importing a uniqueness result from the authors' own prior work.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities or free fitting parameters. The main assumptions are the standard reduced-state treatment of channel memory, the restriction to U(1)-symmetric quadratic models, and the unproved monotonicity of the memory factor. The completeness-relation reduction is standard math.

assumptions (4)
  • domain assumption Haar averaging over sender states represents unknown previous inputs; the channel state after each use is the reduced density operator obtained by tracing out sender and receiver.
    Used in Eqs. (1)-(3) to define the n-th-use fidelity and the recursion for the channel state. It assumes the memory of the channel is fully captured by its reduced density operator and that new sender/receiver qubits are attached in a product state.
  • domain assumption The Hamiltonian is U(1)-symmetric and maps to a quadratic fermionic model for Eq. (4); the example uses the PST Hamiltonian of Ref. [25].
    Stated in Sec. III: the main formula applies when [H, M_z]=0 and H can be mapped to quadratic fermion models. The free-fermion simplification relies on this.
  • ad hoc to paper Monotonicity of the memory term: 0 ≤ A_{n-1} ≤ A_{n-2} ≤ ... ≤ A_1 ≤ 1 for equal readout timings.
    Asserted without proof after Eq. (11) and used to conclude memory effects are detrimental. The inequality is load-bearing for the paper's main quantitative message but not proven.
  • standard math Use of the completeness relation and unitary commutation to reduce sums over channel sites to amplitudes involving sender and receiver.
    Explicit in Eq. (7), relying on ∑|i><i|=1 and U(t2)U(t1)=U(t1+t2). This is a standard linear algebra identity.

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Pith. "Pith review of Memory effects in repeated uses of quantum channels." pith.science (2026). https://pith.science/paper/RIS4DO7R

@misc{pith2026251105661,
  author       = {Pith},
  title        = {Pith review of: Memory effects in repeated uses of quantum channels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RIS4DO7R}},
  note         = {Machine review of arXiv:2511.05661}
}
abstract

Quantum Information Processing (QIP) tasks can be efficiently formulated in terms of quantum dynamical maps, whose formalism is able to provide the appropriate mathematical representation of the evolution of open quantum systems. A key QIP task is quantum state transfer (QST) aimed at sharing quantum information between distant nodes of a quantum network, enabling, e.g. quantum key distribution and distributed quantum computing. QST has primarily been addressed insofar by resetting the quantum channel after each use, thus giving rise to memoryless channels. Here we consider the case where the quantum channel is continuously used, without implementing time- and resource- consuming resetting operations. We derive a general, analytical expression for the $n^{\mathrm{th}}$-use average QST fidelity for $U(1)$-symmetric channels and apply our formalism to a perfect QST channel in the presence of imperfect readout timing. We show that even relatively small readout timing errors give rise to memory effects which have a highly detrimental impact on subsequent QST tasks.

Figures

Figures reproduced from arXiv: 2511.05661 by the authors.

Figure 1
Figure 1. FIG. 1. A quantum channel (green spheres) for the trans [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Average [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Average fidelity for a fixed readout timing error of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Entanglement distribution for the 1 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Reference graph

Works this paper leans on

50 extracted references · 8 linked inside Pith

  1. [1]

    The channel is initialized in|Ψ⟩ C1 =|000. . .000⟩. At timet 0 = 0, the 1 st qubit of the sender reg- ister, in an arbitrary state|Ψ⟩ S1 = cos θ1 2 |0⟩+ sin θ1 2 eiϕ1 |1⟩, and of the receiver register, in the state|0⟩ R1 , are attached to the channel

  2. [2]

    The whole system is then let to evolve for a timet 2

    The systemS+C+Revolves for a timet 1, when the 1 st sender and receiver qubits are sub- stituted with the 2 nd set, respectively in the states |Ψ⟩S2 = cos θ2 2 |0⟩+ sin θ2 2 eiϕ2 |1⟩and|0⟩ R2 . The whole system is then let to evolve for a timet 2

  3. [3]

    arXiv:2511.05661v1 [quant-ph] 7 Nov 2025 2 FIG

    This procedure is repeated until the whole sender register is transferred to the receiver register. arXiv:2511.05661v1 [quant-ph] 7 Nov 2025 2 FIG. 1. A quantum channel (green spheres) for the trans- fer of quantum information between two quantum registers: a sender register (red spheres) and a receiver register (blue spheres). Our figure of merit is the ...

    arXiv 2025

  4. [4]

    C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbr¨ uggen, D. Sugny, and F. K. Wil- helm, Quantum optimal control in quantum tech- nologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technology9, 10.1140/epjqt/s40507-022-00138-x (2022), arXiv:2205.12110

    arXiv 2022

  5. [5]

    Robledo, L

    L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, High-fidelity projective read- out of a solid-state spin quantum register, Nature477, 574 (2011)

    2011

  6. [6]

    Meier, E

    F. Meier, E. Schwarzhans, P. Erker, and M. Huber, Fun- damental accuracy-resolution trade-off for timekeeping devices, Physical Review Letters131, 220201 (2023), arXiv:2301.05173 [quant-ph]

    arXiv 2023

  7. [7]

    Xuereb, P

    J. Xuereb, P. Erker, F. Meier, M. T. Mitchison, and M. Huber, Impact of Imperfect Timekeeping on Quantum 6 Control, Physical Review Letters131, 160204 (2023)

    2023

  8. [8]

    Meier, Y

    F. Meier, Y. Minoguchi, S. Sundelin, T. J. G. Apollaro, P. Erker, S. Gasparinetti, and M. Huber, Precision is not limited by the second law of thermodynamics, Nature Physics21, 1147 (2025)

    2025

Show all 50 references
  1. [9]

    Navascu´ es, Resetting Uncontrolled Quantum Sys- tems, Physical Review X8, 031008 (2018)

    M. Navascu´ es, Resetting Uncontrolled Quantum Sys- tems, Physical Review X8, 031008 (2018)

    2018

  2. [10]

    Bassman Oftelie, A

    L. Bassman Oftelie, A. De Pasquale, and M. Campisi, Dynamic Cooling on Contemporary Quantum Comput- ers, PRX Quantum5, 030309 (2024)

    2024

  3. [11]

    Bose, Quantum communication through an unmodu- lated spin chain, Phys

    S. Bose, Quantum communication through an unmodu- lated spin chain, Phys. Rev. Lett.91, 207901 (2003)

    2003

  4. [12]

    G. M. Nikolopoulos and I. Jex,Quantum State Transfer and Network Engineering, edited by G. M. Nikolopoulos and I. Jex (Springer Berlin Heidelberg, Berlin, Heidel- berg, 2014)

    2014

  5. [13]

    Banchi, G

    L. Banchi, G. Coutinho, C. Godsil, and S. Severini, Pretty good state transfer in qubit chains—the heisen- berg hamiltonian, Journal of Mathematical Physics58, 032202 (2017)

    2017

  6. [14]

    T. J. G. Apollaro, S. Lorenzo, F. Plastina, M. Con- siglio, and K. ˙Zyczkowski, Entangled States Are Harder to Transfer than Product States, Entropy25, 46 (2022), arXiv:2301.04443

    2022 arXiv

  7. [15]

    Caruso, Quantum channels and memory effects, Re- views of Modern Physics86, 1203 (2014)

    F. Caruso, Quantum channels and memory effects, Re- views of Modern Physics86, 1203 (2014)

    2014

  8. [16]

    F. A. Mele, G. D. Palma, M. Fanizza, V. Giovannetti, and L. Lami, Optical fibers with memory effects and their quantum communication capacities, IEEE Transactions on Information Theory70, 8844 (2024)

    2024

  9. [17]

    Sarovar, T

    M. Sarovar, T. Proctor, K. Rudinger, K. Young, E. Nielsen, and R. Blume-Kohout, Detecting crosstalk errors in quantum information processors, Quantum4, 321 (2020)

    2020

  10. [18]

    Benenti, A

    G. Benenti, A. D’Arrigo, and G. Falci, Enhancement of Transmission Rates in Quantum Memory Channels with Damping, Physical Review Letters103, 020502 (2009)

    2009

  11. [19]

    Caruso, V

    F. Caruso, V. Giovannetti, and G. M. Palma, Teleportation-Induced Correlated Quantum Channels, Physical Review Letters104, 020503 (2010)

    2010

  12. [20]

    F. A. Mele, L. Lami, and V. Giovannetti, Restoring Quantum Communication Efficiency over High Loss Op- tical Fibers, Physical Review Letters129, 180501 (2022)

    2022

  13. [21]

    Bayat, D

    A. Bayat, D. Burgarth, S. Mancini, and S. Bose, Memory effects in spin-chain channels for information transmis- sion, Physical Review A77, 050306 (2008)

    2008

  14. [22]

    Giovannetti, D

    V. Giovannetti, D. Burgarth, and S. Mancini, Communi- cation through a quantum link, Phys. Rev. A79, 012311 (2009)

    2009

  15. [23]

    Bowen and S

    G. Bowen and S. Mancini, Quantum channels with a fi- nite memory, Phys. Rev. A69, 012306 (2004)

    2004

  16. [24]

    Giovannetti, A dynamical model for quantum mem- ory channels, Journal of Physics A: Mathematical and General38, 10989 (2005)

    V. Giovannetti, A dynamical model for quantum mem- ory channels, Journal of Physics A: Mathematical and General38, 10989 (2005)

    2005

  17. [25]

    Donaghey and L

    R. Donaghey and L. W. Shapiro, Motzkin numbers, Jour- nal of Combinatorial Theory, Series A23, 291 (1977)

    1977

  18. [26]

    T. J. G. Apollaro, S. Lorenzo, F. Plastina, M. Con- siglio, and K. ˙Zyczkowski, Quantum transfer of interact- ing qubits, New Journal of Physics24, 083025 (2022), arXiv:2205.01579

    2022 arXiv

  19. [27]

    E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Annals of Physics16, 407 (1961)

    1961

  20. [28]

    Christandl, N

    M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Perfect State Transfer in Quantum Spin Networks, Phys- ical Review Letters92, 187902 (2004)

    2004

  21. [29]

    Vinet and A

    L. Vinet and A. Zhedanov, How to construct spin chains with perfect state transfer, Physical Review A85, 012323 (2012)

    2012

  22. [30]

    Christandl, L

    M. Christandl, L. Vinet, and A. Zhedanov, Analytic next- to-nearest-neighbor X X models with perfect state trans- fer and fractional revival, Physical Review A96, 032335 (2017)

    2017

  23. [31]

    X. Li, Y. Ma, J. Han, T. Chen, Y. Xu, W. Cai, H. Wang, Y. P. Song, Z. Y. Xue, Z. Q. Yin, and L. Sun, Per- fect Quantum State Transfer in a Superconducting Qubit Chain with Parametrically Tunable Couplings, Physical Review Applied10, 1 (2018), arXiv:1806.03886

    2018 arXiv

  24. [32]

    R. J. Chapman, M. Santandrea, Z. Huang, G. Corrielli, A. Crespi, M.-H. Yung, R. Osellame, and A. Peruzzo, Experimental perfect state transfer of an entangled pho- tonic qubit, Nature Communications7, 11339 (2016)

    2016

  25. [33]

    Christandl, N

    M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Perfect transfer of arbitrary states in quantum spin networks, Physical Review A71, 032312 (2005)

    2005

  26. [34]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of Mod- ern Physics81, 865 (2009)

    2009

  27. [35]

    Chitambar, D

    E. Chitambar, D. Leung, L. Manˇ cinska, M. Ozols, and A. Winter, Everything you always wanted to know about locc (but were afraid to ask), Communications in Math- ematical Physics328, 891 (2014)

    2014

  28. [36]

    Bengtsson and K

    I. Bengtsson and K. Zyczkowski,Geometry of Quantum States(Cambridge University Press, Cambridge, 2017)

    2017

  29. [37]

    Lorenzo, F

    S. Lorenzo, F. Plastina, M. Consiglio, and T. J. G. Apol- laro, Quantum Map Approach to Entanglement Trans- fer and Generation in Spin Chains (2022) pp. 321–340, arXiv:2112.02348

    2022 arXiv

  30. [38]

    Bose, Quantum communication through spin chain dynamics: an introductory overview, Contemporary Physics48, 13 (2007), https://doi.org/10.1080/00107510701342313

    S. Bose, Quantum communication through spin chain dynamics: an introductory overview, Contemporary Physics48, 13 (2007), https://doi.org/10.1080/00107510701342313

    2007 doi

  31. [39]

    Khatri, K

    S. Khatri, K. Sharma, and M. M. Wilde, Information- theoretic aspects of the generalized amplitude-damping channel, Phys. Rev. A102, 012401 (2020)

    2020

  32. [40]

    Devetak and P

    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)

    2005

  33. [41]

    Pucha la, K

    Z. Pucha la, K. Korzekwa, R. Salazar, P. Horodecki, and K. ˙Zyczkowski, Dephasing superchannels, Phys. Rev. A 104, 052611 (2021)

    2021

  34. [42]

    M. M. Wolf and D. P´ erez-Garc ´ ıa, Quantum capacities of channels with small environment, Phys. Rev. A75, 012303 (2007)

    2007

  35. [43]

    Barnum, M

    H. Barnum, M. A. Nielsen, and B. Schumacher, Infor- mation transmission through a noisy quantum channel, Phys. Rev. A57, 4153 (1998)

    1998

  36. [44]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information, 10th ed. (Cambridge Univer- sity Press, Cambridge, 2010)

    2010

  37. [45]

    W. K. Wootters, Entanglement of formation of an arbi- trary state of two qubits, Physical Review Letters80, 2245 (1998), arXiv:quant-ph/9709029

    1998 arXiv

  38. [46]

    Kay, Perfect state transfer: Beyond nearest-neighbor 7 couplings, Physical Review A - Atomic, Molecular, and Optical Physics73, 1 (2006)

    A. Kay, Perfect state transfer: Beyond nearest-neighbor 7 couplings, Physical Review A - Atomic, Molecular, and Optical Physics73, 1 (2006)

    2006

  39. [47]

    T. J. G. Apollaro, L. Banchi, A. Cuccoli, R. Vaia, and P. Verrucchi, 99 % -fidelity ballistic quantum-state trans- fer through long uniform channels, Physical Review A85, 052319 (2012)

    2012

  40. [48]

    Ronke, M

    R. Ronke, M. P. Estarellas, I. D’Amico, T. P. Spiller, and T. Miyadera, Anderson localisation in spin chains for perfect state transfer, The European Physical Journal D 70, 189 (2016)

    2016

  41. [49]

    J. Zhou, M. Li, W. Wang, W. Cai, Z. Hua, Y. Xu, X. Pan, G. Xue, H. Zhang, Y. Song, H. Yu, C.-L. Zou, and L. Sun, Quantum State Transfer between Superconducting Cavi- ties via Exchange-Free Interactions, Physical Review Let- ters133, 220801 (2024)

    2024

  42. [50]

    Junior, G

    M. Junior, G. Almeida, and F. De Moura, Quantum state transfer in ladder systems with cross-correlated disorder, Physica E: Low-dimensional Systems and Nanostructures 171, 116249 (2025)

    2025

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