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A unified approach to quantum resource theories and a new class of free operations

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Pith's one-line read The paper claims that every quantum resource theory is defined by a preferred algebraic structure whose automorphisms are the free operations, and that complexifying the Lie algebra yields a new class of resource non-increasing operations.

desk verdict Fresh CFO construction worth engaging, but the free-state preservation theorem is narrower than the abstract claims. read the letter →

arxiv 2507.10851 v1 pith:WWQC3L45 submitted 2025-07-14 quant-ph

N. L. Diaz , Antonio Anna Mele , Pablo Bermejo , Paolo Braccia , Andrew E. Deneris , Martin Larocca , M. Cerezo This is my paper
classification quant-ph MSC 81P4517B2022E70
keywords quantumresourcetheoriesfreeoperationsautomorphismscomplexificationLiealgebrasSLOCCspincoherencefermionicGaussianity
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

This paper argues that every quantum resource theory (QRT) is fixed by a single choice: a preferred algebraic structure $\mathcal{E}$ that must be preserved, so that the free operations are exactly the automorphisms of $\mathcal{E}$. The same recipe reproduces standard free operations for entanglement, Clifford stabilizerness, purity, imaginarity, fermionic Gaussianity, reference frames, thermodynamics, and coherence, where $\mathcal{E}$ can be a Lie algebra, a group, a ring, or an unstructured set. The paper then exports the entanglement lesson that moving from local unitaries to stochastic local operations is nothing but complexification: for any Lie-algebra-based QRT, complexifying the Lie algebra $\mathfrak{g}$ to $\mathbb{C}\mathfrak{g}$ generates a new class of complexified free operations (CFOs). Theorem 1 proves that CFOs map free states to free states, and Theorem 2 shows that in the spin-coherence QRT every operation in $\mathrm{GL}(2)$ strictly increases the $\mathfrak{g}$-purity of a weight state unless the state is already free. The framework thus supplies a systematic answer to the open problem of defining resource non-increasing operations in Lie-algebraic theories such as fermionic Gaussianity.

What carries the argument

The engine is the pair: (i) the preferred algebraic structure $\mathcal{E}=(S,A)$ with its automorphism group $\mathrm{Aut}(\mathcal{E})$ acting via the adjoint representation, which prescribes the free operations and hence the free states as minimal orbits; and (ii) the complexification step $\mathfrak{g}\mapsto\mathbb{C}\mathfrak{g}=\mathfrak{g}\oplus i\mathfrak{g}$, which produces the complexified free operations $G_{\mathrm{CFO}}=e^{\mathbb{C}\mathfrak{g}}$ for any Lie-algebra-based QRT. The proof of Theorem 1 uses the Iwasawa decomposition of $M\in e^{\mathbb{C}\mathfrak{g}}$ as $M = U e^{\sum_i \alpha_i h_i} e^{\sum_j x_j e_j^+}$; the raising operators $e_j^+$ annihilate the highest-weight state, so every CFO sends the free set into itself. The resource monotonicity is carried by the $\mathfrak{g}$-purity $P(\rho)=\frac{1}{N_{\mathfrak{g}}}\sum_i \mathrm{Tr}[\rho g_i]^2$, whose closed-form evaluation on $\mathfrak{su}(2)$ weight states in terms of hypergeometric functions yields the inequality of Theorem 2.

What would settle it

For Theorem 1: find a Lie-algebra-based QRT whose free states are defined operationally, for instance as the states preparable by a restricted set of channels, and exhibit a CFO channel that maps one of those free states to a state outside the free set. For Conjecture 1: search for a single state in $\mathfrak{su}(2)$ or $\mathfrak{so}(2n)$ and a CFO channel for which the average $\mathfrak{g}$-purity after the channel is strictly smaller than the initial purity; such a counterexample would refute the monotonicity-on-average claim.

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Extended reading notes

Core claim

The central claim is that a quantum resource theory is characterized by a preferred algebraic structure $\mathcal{E} = (S, A)$, with $S$ a set of privileged operators and $A$ a set of algebraic operations, and that the free operations are the automorphisms of $\mathcal{E}$ under the adjoint action. The paper identifies $\mathcal{E}$ explicitly for eight standard QRTs: a Lie algebra for entanglement ($\mathfrak{u}(H_A) \oplus \mathfrak{u}(H_B)$), purity, imaginarity, fermionic Gaussianity ($\mathfrak{so}(2n)$), spin coherence ($\mathfrak{su}(2)$), and reference frames; the Pauli group for Clifford stabilizerness; the ring of diagonal matrices for coherence; and a bare Hamiltonian for thermodynamics. Its new constructive result is that for Lie-algebraic QRTs, complexifying the algebra turns unitary free operations (UFOs) into complexified free operations (CFOs) $G_{\mathrm{CFO}} = e^{\mathbb{C}\mathfrak{g}}$, in the same way that complexifying $\mathfrak{u}(H_A)\oplus\mathfrak{u}(H_B)$ to $\mathfrak{gl}(H_A)\oplus\mathfrak{gl}(H_B)$ turns local unitaries into SLOCC for entanglement. Theorem 1 states that CFOs map free states to free states, $\mathrm{Adj}\,G_{\mathrm{CFO}}:\mathcal{F}\to\mathcal{F}$ up to normalization, where free states are the orbit of the highest-weight state under the unitary free operations together with convex mixtures. Theorem 2 states that for spin coherence every $M\in \mathrm{GL}(2)=e^{\mathbb{C}\mathfrak{su}(2)}$ is resource non-increasing as measured by the $\mathfrak{su}(2)$-purity, with equality only on the free weight states $m=\pm s$.

Load-bearing premise

The central theorem holds only if free states are defined as the orbit of the highest-weight state under the unitary free operations together with mixtures; the paper itself notes this is a rule of thumb that fails for the imaginarity resource theory, so a different operational definition of free states would break the proof.

Editorial extensions

If this is right

  • Every QRT can be specified by naming the structure to preserve; free operations then follow as its automorphisms and free states as minimal orbits under them.
  • For every Lie-algebra-based QRT, CFOs give a concrete family of resource non-increasing operations implementable by sequential weak measurements, resolving the open problem of defining such operations for theories like fermionic Gaussianity.
  • In spin coherence, acting on a weight state $|s,m\rangle$ with any $M\in\mathrm{GL}(2)$ strictly increases the $\mathfrak{g}$-purity unless $m=\pm s$, so resource never increases and free states map to free states.
  • Numerical evidence on $\mathfrak{su}(2)$ and $\mathfrak{so}(2n)$ supports the conjecture that CFO channels do not increase resource on average for arbitrary states, not just weight states.
  • The framework collapses the entanglement and scrambling QRTs into one: both come from $\mathfrak{u}(\sqrt{d})\oplus\mathfrak{u}(\sqrt{d})$, with scrambling adding the outer SWAP automorphism.

Reading between the lines

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

  • Extension: if the automorphism principle is taken as the definition of a QRT, new resource theories can be generated mechanically from any algebraic structure with a computable automorphism group; testing it on Jordan algebras or $C^*$-algebras would show whether the recipe generalizes beyond the examples treated here.
  • Extension: the mechanism behind Theorem 2 – the Cartan part of the Iwasawa decomposition raises the purity along the $J_z$ direction while the off-diagonal part adds a non-negative correction – suggests the monotonicity holds for weight states of every compact simple Lie algebra, not just $\mathfrak{su}(2)$; this is a natural but unproven extension.
  • Extension: because the paper ties CFOs to sequential isotropic weak measurements, one testable consequence is that the set of CFO channels exactly coincides with the set of channels realizable by such measurements, which would give the algebraic construction a direct operational meaning.
  • Extension: since the automorphisms of the Pauli group are larger than the Clifford group, the framework suggests a new stabilizerness resource theory whose free operations are all Pauli-group automorphisms, potentially exhibiting a gap analogous to LOCC versus SLOCC.
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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

4 major / 4 minor

Summary. The paper proposes that a quantum resource theory (QRT) can be defined by a preferred algebraic structure E—a set, a Lie algebra, a group, or a ring—whose automorphism group under the adjoint action plays the role of the free operations. It identifies E for thermodynamics, Clifford stabilizerness, coherence, bipartite entanglement and scrambling, purity, imaginarity, fermionic Gaussianity, spin coherence, and reference frames. On this basis, the paper introduces complexified free operations (CFOs) e^{Cg} for Lie-algebra QRTs, proves in Theorem 1 that CFOs preserve the convex hull of the orbit of the highest weight state under unitary free operations for semisimple compact Lie algebras, proves in Theorem 2 an analytic g-purity monotonicity statement for su(2) weight states, and formulates Conjecture 1 on average g-purity monotonicity for general pure states, with numerical evidence for spin coherence and fermionic Gaussianity.

Significance. If the central claims held at the advertised level, the paper would provide a unifying principle for QRTs and a systematic prescription for constructing non-unitary free operations, addressing an open problem raised in Ref. [48]. The paper's concrete strengths are the explicit SM proofs of Theorems 1 and 2, the explicit construction of trace-preserving channels approximating CFOs via sequential weak measurements in SM §II, and the breadth of examples spanning very different QRTs. The su(2) weight-state result is a nontrivial analytic monotonicity statement. However, as detailed below, the scope of Theorem 1 is narrower than the paper's central claim, the monotonicity for general states remains conjectural, and the unifying Claim I is a post-hoc definitional observation rather than a theorem derived from operational principles.

major comments (4)
  1. [Theorem 1 / SM §I.A; main text 'rule of thumb' and footnote 3] The proof of Theorem 1 in SM §I.A defines the free set F as the orbit of the highest weight state under G_UFO together with convex combinations. The main text introduces this identification only as a 'rule of thumb' satisfied by '(most of) the QRTs studied,' and footnote 3 explicitly concedes that the imaginarity QRT has free states that are not generalized coherent states. Reference frames, also listed as a Lie-algebra QRT, have free states that are group-invariant states rather than highest-weight orbits. Therefore Theorem 1 does not establish that CFOs preserve the actual free-state set for the full advertised family of Lie-algebra QRTs. The paper should either restrict the scope of this claim, including the abstract, to QRTs whose free states are coherent-state orbits and their convex hulls, or provide an additional argument covering the other free-state definitions.
  2. [Theorem 1, SM Lemma 1; Eq. (1) and the general Lie-algebra paragraph] Theorem 1 and its proof are stated for semisimple compact Lie algebras, but several examples advertised in the paper are not semisimple: Eq. (1) is u(H_A) ⊕ u(H_B), and the general Lie-algebra paragraph explicitly allows an abelian ideal, hence u(1)-containing algebras. The proof of SM Lemma 1 uses the Iwasawa decomposition of the complexified semisimple algebra and does not, as written, apply to reductive algebras with nontrivial center. The authors should state clearly which of the listed QRTs are covered by Theorem 1, and either extend the proof to the reductive case or remove the uncovered examples from the scope of the theorem.
  3. [Definition I, Conjecture 1, and the abstract] The paper calls CFOs 'genuine free operations' on the basis of Theorem 1, but resource monotonicity is not proven for general states. The only analytic monotonicity result is Theorem 2, which covers weight states of su(2); for arbitrary states the average monotonicity of the g-purity is Conjecture 1, supported by numerical simulations for only two QRTs. Consequently, the abstract's statement that the paper 'rigorously proves that they map free states to free states, as well as determine more general situations where these transformations strictly do not increase the resource' is accurate only for free-state preservation under the Theorem 1 hypothesis and for the su(2) weight-state case. The claims about resource non-increase and about solving the open problem for general Lie-algebra QRTs should be qualified accordingly.
  4. [Claim I and the Clifford-stabilizerness paragraph] Claim I is presented as the first result, but its status is that of a definitional observation: free operations are set to be automorphisms of an E that is chosen, for each example, so that the automorphisms coincide with known free operations. The paper itself notes mismatches: footnote 1 states that only automorphisms fixing the center recover the Clifford group, and footnote 2 notes that LOCC and SLOCC differ from the axiomatic groups. To make the unification predictive rather than post-hoc, the paper should state explicitly what counts as a success condition for Claim I and discuss which QRTs require additional restrictions beyond Aut(E).
minor comments (4)
  1. [Theorem 2 statement] Theorem 2 states G_CFO = GL(2) = e^{Csu(2)}, but the exponential of sl(2,C) is SL(2,C), not GL(2,C); since global scalars cancel in the normalized state and in the g-purity, this should be clarified as a projective statement.
  2. [SM Eq. (18) and Eq. (19)] The closed-form expressions for the g-purity are quite dense; it would help readers if the admissible ranges of α, η, and z were stated immediately before Eq. (18), and if the definition z = -e^{2α}|η|^2 were repeated near Eq. (19) where it is first used.
  3. [SM §II, Eq. (21)] The construction of Kraus operators in Eq. (21) is said to approximate elements of e^{Cg} for small ε; a precise convergence statement, including the operator-norm sense in which the approximation holds as N increases at fixed T, would make the claim of experimental accessibility more rigorous.
  4. [Footnote 3] The exception of imaginarity noted in footnote 3 should be integrated into the main-text definition of free states, so that the reader is not led to believe Theorem 1 applies uniformly to all Lie-algebra QRTs listed in the preceding paragraph.

Circularity Check

1 steps flagged · score 4.0 of 10

Main circular element is the post-hoc fit of E to known free operations; the CFO theorems themselves are derived, not circular, but Theorem 1's advertised scope is broader than its coherent-state definition supports.

  1. self definitional [Abstract and 'Unifying framework' (Claim I); 'Entanglement (LU)' example]
    "In this work, we continue the quest to unify QRTs. In particular, we show that QRTs can be defined in terms of some preferred algebraic structure E that must be preserved (see Fig. 1). As such, starting from E, the free operations follow as its automorphisms, which in turn leads to natural notions of free states."

    The paper simultaneously presents E as the origin of the free operations and 'determines' E per QRT from the already-known free operations. For example, for LU entanglement it defines E = u(H_A) ⊕ u(H_B) and notes the automorphisms are U(H_A) ⊗ U(H_B), i.e., exactly the known local unitaries; for coherence it defines E = D_d(R) so automorphisms are generalized permutations. Thus 'free operations follow from E' holds only because each E was calibrated so that Aut(E) matches the pre-existing free-operation set. The claimed explanation is therefore a post-hoc fit: the output (free ops) is used to select the input (E), making the 'derivation' circular as an account of why those operations are free.

full rationale

The main new mathematical contribution, the CFO construction and Theorems 1 and 2, is not circular. Theorem 1 is proven from the Iwasawa decomposition and the annihilation of the highest weight by raising operators, so it genuinely derives preservation of the coherent-state free set rather than assuming it as a premise; Theorem 2 proceeds by an explicit closed-form hypergeometric computation. The principal circularity sits one level up: the paper's unifying principle 'QRTs follow from a preferred algebraic structure E' is supported only by choosing E for each QRT so that its automorphisms reproduce the already-known free operations. That is a post-hoc identification, not an independent derivation. The review should also note scope limitations that are not themselves circular: footnote 3 concedes that imaginarity free states are not generalized coherent states, and Theorem 1 is stated for semisimple compact Lie algebras, while several listed examples are not semisimple. These caveats narrow the claim but do not turn the CFO proofs into circular arguments, so the overall score is moderate rather than severe.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claims rest on standard Lie theory (Iwasawa decomposition, Cartan-Weyl basis) and on the assumption that free states are highest-weight orbits. No new physical entities are introduced.

assumptions (6)
  • standard math For semi-simple compact Lie algebras, the Iwasawa decomposition holds for the complexified algebra.
    Used in Supplemental Lemma 1 to factor any M in e^{Cg} into unitary, Cartan, and positive-root parts.
  • standard math A Cartan-Weyl basis exists, and the highest weight vector is annihilated by all raising operators e+_j.
    Core to the proof of Theorem 1 (Eq. 4), where the e+ terms drop out on the highest weight state.
  • domain assumption Free states in Lie-algebra QRTs are the orbit of the highest weight state under UFOs, plus convex mixtures.
    Stated in the main text as a 'rule of thumb'; footnote 3 notes imaginarity is an exception. Theorem 1's conclusion depends on this definition.
  • domain assumption The Lie algebra g is at most a sum of an abelian and a non-abelian ideal.
    The main text restricts to this case when presenting the general Lie-algebra framework; it excludes more general Lie algebras.
  • domain assumption CFOs can be realized by sequential continuous weak measurements.
    Cited from Refs. [67,68]; used to argue experimental accessibility but not needed for the formal resource-theory statements.
  • standard math Hypergeometric function identities and positivity properties used in Theorem 2's proof are valid for z ≤ 0.
    The closed-form Eq. (19) and the bound rely on these standard analytic facts.

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Pith. "Pith review of A unified approach to quantum resource theories and a new class of free operations." pith.science (2026). https://pith.science/paper/WWQC3L45

@misc{pith2026250710851,
  author       = {Pith},
  title        = {Pith review of: A unified approach to quantum resource theories and a new class of free operations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WWQC3L45}},
  note         = {Machine review of arXiv:2507.10851}
}
abstract

In quantum resource theories (QRTs) certain quantum states and operations are deemed more valuable than others. While the determination of the ``free'' elements is usually guided by the constraints of some experimental setup, this can make it difficult to study similarities and differences between QRTs. In this work, we argue that QRTs follow from the choice of a preferred algebraic structure $\mathcal{E}$ to be preserved, thus setting the free operations as the automorphisms of $\mathcal{E}$. We illustrate our finding by determining $\mathcal{E}$ for the QRTs of entanglement, Clifford stabilizerness, purity, imaginarity, fermionic Gaussianity, reference frames, thermodynamics and coherence; showing instances where $\mathcal{E}$ is a Lie algebra, group, ring, or even a simple set. This unified understanding allows us to generalize the concept of stochastic local operations and classical communication (SLOCC) to identify novel resource non-increasing operations for Lie-algebra based QRTs, thus finding a new solution to an open problem in the literature. We showcase the sanity of our new set of operations by rigorously proving that they map free states to free states, as well as determine more general situations where these transformations strictly do not increase the resource of a state.

Figures

Figures reproduced from arXiv: 2507.10851 by the authors.

Figure 1
Figure 1. Schematic representation of our results. a) We show that preserved algebraic structures underlie QRTs. We identify such structure for some of the most studied QRTs, find￾ing that it can be a vector space (Lie algebra), group, ring or even just a set. (b) By identifying the complexification as the mechanism which promotes local unitaries (LU) to stochastic local operations and classical communication (SLOCC) in the Q… view at source ↗
Figure 2
Figure 2. Change in g-Purity under CFOs for the QRT of spin coherence. Here we show the algebraic purity for 104 (normalized) states M|s, m⟩ with M ∈ GCFO = GL(2) for s = 5 and for the indicated values of m. The inner (outer) circle cor￾responds to g-Purity equal to zero (one). As per Theorem 2, the action of M can only strictly decrease the resourcefulness– increase the g-Purity [70]– of the state with respect to the start￾i… view at source ↗
Figure 3
Figure 3. Numerical evidence of conjecture 1. The red cir￾cles (orange triangles) represent the su(2)-purity (so(2n)-purity) of 150 initial random states–ordered by their purity–in QRT of spin coherence for s = 5 (fermionic Gaussianity for n = 8 qubits). The blue squares (purple diamonds) are the average purity after acting with a CFO channel on these states. Ar￾rows show the direction of change in the purity (i.e., CFOs only… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Purity of different weight states after acting with a CFO parameterized by α, η. Here s = 5 and η is taken as real (equivalent to considering the absolute value, see Eq. (19)). The curves correspond to P(|ψ ′ ⟩) while the planes correspond to P(|s, m⟩) with the two mat…

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Reference graph

Works this paper leans on

73 extracted references · 59 canonical work pages · cited by 4 Pith papers

  1. [48]

    Barnum, E

    H. Barnum, E. Knill, G. Ortiz, and L. Viola, Generaliza- tions of entanglement based on coherent states and convex sets, Physical Review A68, 032308 (2003)

    work page 2003

  2. [1]

    A. C. Costa and R. M. Angelo, Information-based approach towards a unified resource theory, Quantum Information Processing 19, 325 (2020)

    work page 2020

  3. [2]

    Coecke, T

    B. Coecke, T. Fritz, and R. W. Spekkens, A mathematical theory of resources, Information and Computation250, 59 (2016)

    work page 2016

  4. [3]

    Chitambar and G

    E. Chitambar and G. Gour, Quantum resource theories, Reviews of modern physics91, 025001 (2019)

    2019

  5. [4]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Reviews of modern physics81, 865 (2009)

    2009

  6. [5]

    M. B. Plenio and S. Virmani, An introduction to entangle- ment measures, Quantum Info. Comput.7, 1–51 (2007)

    work page 2007

  7. [6]

    J. L. Beckey, N. Gigena, P. J. Coles, and M. Cerezo, Com- putable and operationally meaningful multipartite entan- glement measures, Phys. Rev. Lett.127, 140501 (2021)

    2021

  8. [7]

    Contreras-Tejada, C

    P. Contreras-Tejada, C. Palazuelos, and J. I. De Vicente, Resource theory of entanglement with a unique multipar- tite maximally entangled state, Physical review letters122, 120503 (2019)

    work page 2019

Show all 73 references
  1. [8]

    E. Kaur, S. Das, M. M. Wilde, and A. Winter, Resource theory of unextendibility and nonasymptotic quantum ca- pacity, Physical Review A104, 022401 (2021)

    2021

  2. [9]

    R. J. Garcia, K. Bu, and A. Jaffe, Resource theory of quan- tum scrambling, Proceedings of the National Academy of Sciences 120, e2217031120 (2023)

    2023

  3. [10]

    Veitch, S

    V. Veitch, S. H. Mousavian, D. Gottesman, and J. Emer- son, The resource theory of stabilizer quantum computa- tion, New Journal of Physics16, 013009 (2014)

    2014

  4. [11]

    Howard and E

    M. Howard and E. Campbell, Application of a resource the- ory for magic states to fault-tolerant quantum computing, Physical review letters118, 090501 (2017)

    2017

  5. [12]

    Leone and L

    L. Leone and L. Bittel, Stabilizer entropies are mono- tones for magic-state resource theory, arXiv preprint arXiv:2404.11652 (2024)

    2024 arXiv

  6. [13]

    Horodecki, P

    M. Horodecki, P. Horodecki, and J. Oppenheim, Reversible transformations from pure to mixed states and the unique measure of information, Physical Review A 67, 062104 (2003)

    2003

  7. [14]

    Streltsov, H

    A. Streltsov, H. Kampermann, S. Wölk, M. Gessner, and D. Bruß, Maximal coherence and the resource theory of purity, New Journal of Physics20, 053058 (2018)

    2018

  8. [15]

    G. Gour, M. P. Müller, V. Narasimhachar, R. W. Spekkens, and N. Y. Halpern, The resource theory of informational nonequilibrium in thermodynamics, Physics Reports583, 1 (2015)

    2015

  9. [16]

    Luo and Y

    Y. Luo and Y. Li, Robustness of purity: an operational ap- proach to resource theory of purity, The European Physical Journal D73, 1 (2019)

    2019

  10. [17]

    Hickey and G

    A. Hickey and G. Gour, Quantifying the imaginarity of quantum mechanics, Journal of Physics A: Mathematical and Theoretical51, 414009 (2018)

    2018

  11. [18]

    K.-D. Wu, T. V. Kondra, S. Rana, C. M. Scandolo, G.- Y. Xiang, C.-F. Li, G.-C. Guo, and A. Streltsov, Resource theory of imaginarity: Quantification and state conversion, Physical Review A103, 032401 (2021)

    2021

  12. [19]

    K.-D. Wu, T. V. Kondra, S. Rana, C. M. Scandolo, G.- Y. Xiang, C.-F. Li, G.-C. Guo, and A. Streltsov, Opera- tional resource theory of imaginarity, Physical Review Let- ters 126, 090401 (2021)

    2021

  13. [20]

    Gigena and R

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

    2015

  14. [21]

    Weedbrook, S

    C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Reviews of Modern Physics84, 621 (2012)

    2012

  15. [22]

    Hebenstreit, R

    M. Hebenstreit, R. Jozsa, B. Kraus, S. Strelchuk, and M. Yoganathan, All pure fermionic non-gaussian states are magic states for matchgate computations, Physical review letters 123, 080503 (2019)

    2019

  16. [23]

    N. L. Diaz, D. García-Martín, S. Kazi, M. Larocca, and M. Cerezo, Showcasing a barren plateau theory beyond the dynamical lie algebra, arXiv preprint arXiv:2310.11505 (2023)

    2023 arXiv

  17. [24]

    Jozsa and A

    R. Jozsa and A. Miyake, Matchgates and classical simula- tion of quantum circuits, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences464, 3089 (2008)

    2008

  18. [25]

    A. A. Mele and Y. Herasymenko, Efficient learning of quan- tum states prepared with few fermionic non-gaussian gates, PRX Quantum6, 010319 (2025)

    2025

  19. [26]

    B.DiasandR.Koenig,Classicalsimulationofnon-gaussian fermionic circuits, Quantum8, 1350 (2024)

    2024

  20. [27]

    M. L. Goh, M. Larocca, L. Cincio, M. Cerezo, and F. Sauvage, Lie-algebraic classical simulations for quantum computing, arXiv preprint arXiv:2308.01432 (2023)

    2023

  21. [28]

    D. J. Brod and E. F. Galvao, Extending matchgates into universal quantum computation, Physical Review A—Atomic, Molecular, and Optical Physics 84, 022310 (2011)

    2011

  22. [29]

    Robert and M

    D. Robert and M. Combescure,Coherent states and appli- cations in mathematical physics (Springer, 2021)

    2021

  23. [30]

    A. M. Perelomov, Generalized coherent states and some of their applications, Soviet Physics Uspekhi20, 703 (1977)

    1977

  24. [31]

    Zhang, R

    W.-M. Zhang, R. Gilmore,et al., Coherent states: Theory and some applications, Reviews of Modern Physics62, 867 (1990)

    1990

  25. [32]

    J. A. Vaccaro, F. Anselmi, H. M. Wiseman, and K. Ja- cobs, Tradeoff between extractable mechanical work, ac- cessible entanglement, and ability to act as a reference sys- tem, under arbitrary superselection rules, Physical Review A—Atomic, Molecular, and Optical Physics 77, 03...

    2008

  26. [33]

    Gour and R

    G. Gour and R. W. Spekkens, The resource theory of quan- tum reference frames: manipulations and monotones, New Journal of Physics10, 033023 (2008)

    2008

  27. [34]

    Marvian and R

    I. Marvian and R. W. Spekkens, The theory of manipula- tions of pure state asymmetry: I. basic tools, equivalence 7 classes and single copy transformations, New Journal of Physics 15, 033001 (2013)

    2013

  28. [35]

    Marvian, R

    I. Marvian, R. W. Spekkens, and P. Zanardi, Quantum speed limits, coherence, and asymmetry, Physical Review A 93, 052331 (2016)

    2016

  29. [36]

    T.MartinelliandD.O.Soares-Pinto,Quantifyingquantum reference frames in composed systems: Local, global, and mutual asymmetries, Physical Review A99, 042124 (2019)

    2019

  30. [37]

    Goold, M

    J. Goold, M. Huber, A. Riera, L. Del Rio, and P. Skrzypczyk, The role of quantum information in thermo- dynamics—a topical review, Journal of Physics A: Mathe- matical and Theoretical49, 143001 (2016)

    2016

  31. [38]

    Lostaglio, An introductory review of the resource the- ory approach to thermodynamics, Reports on Progress in Physics 82, 114001 (2019)

    M. Lostaglio, An introductory review of the resource the- ory approach to thermodynamics, Reports on Progress in Physics 82, 114001 (2019)

    2019

  32. [39]

    N. H. Y. Ng and M. P. Woods, Resource theory of quantum thermodynamics: Thermal operations and second laws, in Thermodynamics in the quantum regime: Fundamental as- pects and new directions (Springer, 2019) pp. 625–650

    2019

  33. [40]

    Streltsov, G

    A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: Quantum coherence as a resource, Reviews of Modern Physics 89, 041003 (2017)

    2017

  34. [41]

    Saxena, E

    G. Saxena, E. Chitambar, and G. Gour, Dynamical re- source theory of quantum coherence, Physical Review Re- search 2, 023298 (2020)

    2020

  35. [42]

    K.-D. Wu, T. Theurer, G.-Y. Xiang, C.-F. Li, G.-C. Guo, M. B. Plenio, and A. Streltsov, Quantum coherence and state conversion: theory and experiment, npj Quantum In- formation 6, 22 (2020)

    2020

  36. [43]

    Winter and D

    A. Winter and D. Yang, Operational resource theory of coherence, Physical review letters116, 120404 (2016)

    2016

  37. [44]

    Ma, Quantifying coherence and entanglement via simple measurements, arXiv preprint arXiv:1707.09928 (2017)

    G.Smith, J.A.Smolin, X.Yuan, Q.Zhao, D.Girolami,and X. Ma, Quantifying coherence and entanglement via simple measurements, arXiv preprint arXiv:1707.09928 (2017)

    2017 arXiv

  38. [45]

    Heimendahl, M

    A. Heimendahl, M. Heinrich, and D. Gross, The axiomatic and the operational approaches to resource theories of magic do not coincide, Journal of Mathematical Physics 63, 10.1063/5.0085774 (2022)

    2022 doi

  39. [46]

    Koashi, F

    M. Koashi, F. Takenaga, T. Yamamoto, and N. Imoto, ‘quantum nonlocality without entanglement’in a pair of qubits, in Workshop on Entanglement and Quantum De- coherence (Optica Publishing Group, 2008) p. P4

    2008

  40. [47]

    R. Duan, Y. Feng, Y. Xin, and M. Ying, Distinguishability of quantum states by separable operations, IEEE Transac- tions on Information Theory55, 1320 (2009)

    2009

  41. [49]

    Barnum, E

    H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, A subsystem-independent generalization of entanglement, Physical Review Letters92, 107902 (2004)

    2004

  42. [50]

    Viola and W

    L. Viola and W. G. Brown, Generalized entanglement as a framework for complex quantum systems: purity versus de- localization measures, Journal of Physics A: Mathematical and Theoretical40, 8109 (2007)

    2007

  43. [51]

    Y. S. Weinstein and L. Viola, Generalized entanglement as a natural framework for exploring quantum chaos, Euro- physics Letters76, 746 (2006)

    2006

  44. [52]

    Gilmore, On the properties of coherent states, Revista Mexicana de Física23, 143 (1974)

    R. Gilmore, On the properties of coherent states, Revista Mexicana de Física23, 143 (1974)

    1974

  45. [53]

    Delbourgo and J

    R. Delbourgo and J. Fox, Maximum weight vectors possess minimal uncertainty, Journal of Physics A: Mathematical and General10, L233 (1977)

    1977

  46. [54]

    Kostant and S

    B. Kostant and S. Sternberg, Symplectic projective orbits, in New Directions in Applied Mathematics: Papers Pre- sented April 25/26, 1980, on the Occasion of the Case Cen- tennial Celebration (Springer, 1982) pp. 81–84

    1980

  47. [55]

    Planat and M

    M. Planat and M. Kibler, Unitary reflection groups for quantumfaulttolerance,Journalofcomputationalandthe- oretical nanoscience7, 1759 (2010)

    2010

  48. [56]

    Clark, R

    S. Clark, R. Jozsa, and N. Linden, Generalised clifford groups and simulation of associated quantum circuits, arXiv preprint quant-ph/0701103 10.48550/arXiv.quant- ph/0701103 (2007)

    2007 doi arXiv

  49. [57]

    Gottesman, Theory of fault-tolerant quantum computa- tion, Physical Review A57, 127 (1998)

    D. Gottesman, Theory of fault-tolerant quantum computa- tion, Physical Review A57, 127 (1998)

    1998

  50. [58]

    Mastel, The clifford theory of then-qubit clifford group, arXiv preprint arXiv:2307.05810 (2023)

    K. Mastel, The clifford theory of then-qubit clifford group, arXiv preprint arXiv:2307.05810 (2023)

    2023

  51. [59]

    1071 (IOP Publish- ing, 2018) p

    J.Tolar,Oncliffordgroupsinquantumcomputing,in Jour- nal of Physics: Conference Series , Vol. 1071 (IOP Publish- ing, 2018) p. 012022

    2018

  52. [60]

    Selinger, Generators and relations for n-qubit clif- ford operators, Logical Methods in Computer Science11, 0.2168/LMCS-11(2:10)2015 (2015)

    P. Selinger, Generators and relations for n-qubit clif- ford operators, Logical Methods in Computer Science11, 0.2168/LMCS-11(2:10)2015 (2015)

    2015

  53. [61]

    C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, Exact and asymptotic measures of mul- tipartite pure-state entanglement, Physical Review A63, 012307 (2000)

    2000

  54. [62]

    Chitambar, D

    E. Chitambar, D. Leung, L. Mančinska, M. Ozols, and A. Winter, Everything you always wanted to know about locc (but were afraid to ask), Communications in Mathe- matical Physics328, 303 (2014)

    2014

  55. [63]

    W. Dür, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Physical Review A62, 062314 (2000)

    2000

  56. [64]

    Miyake, Multipartite entanglement under stochastic lo- cal operations and classical communication, International Journal of Quantum Information2, 65 (2004)

    A. Miyake, Multipartite entanglement under stochastic lo- cal operations and classical communication, International Journal of Quantum Information2, 65 (2004)

    2004

  57. [65]

    A. E. Deneris, P. Braccia, P. Bermejo, A. A. Mele, and M. Cerezo, Analyzing the free states of one quantum re- source theory as resource states of another, Manuscript in preparation (2025)

    2025

  58. [66]

    F. G. Brandao and G. Gour, Reversible framework for quantum resource theories, Physical review letters 115, 070503 (2015)

    2015

  59. [67]

    C. S. Jackson and C. M. Caves, Simultaneous measure- ments of noncommuting observables: Positive transforma- tions and instrumental lie groups, Entropy25, 1254 (2023)

    2023

  60. [68]

    C. S. Jackson and C. M. Caves, How to perform the co- herent measurement of a curved phase space by continuous isotropic measurement. i. spin and the kraus-operator ge- ometry of SL(2, C), Quantum7, 1085 (2023)

    2023

  61. [69]

    Ragone, B

    M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. Ortiz Marrero, M. Larocca, and M. Cerezo, A lie al- 8 gebraic theory of barren plateaus for deep parameter- ized quantum circuits, Nature Communications15, 7172 (2024)

    2024

  62. [70]

    Bermejo, P

    P. Bermejo, P. Braccia, A. A. Mele, N. L. Diaz, A. E. Deneris, M. Larocca, and M. Cerezo, Char- acterizing quantum resourcefulness via group-fourier decompositions, arXiv preprint arXiv:2506.19696 10.48550/arXiv.2506.19696 (2025)

    2025 doi arXiv

  63. [71]

    Shojaee, C

    E. Shojaee, C. S. Jackson, C. A. Riofrío, A. Kalev, and I. H. Deutsch, Optimal pure-state qubit tomography via sequentialweakmeasurements,Physicalreviewletters 121, 130404 (2018)

    2018

  64. [72]

    Coecke and A

    B. Coecke and A. Kissinger, Categorical quantum me- chanics i: causal quantum processes, arXiv preprint arXiv:1510.05468 10.48550/arXiv.1510.05468 (2015)

    2015 doi arXiv

  65. [73]

    A UNIFIED APPROACH TO QUANTUM RESOURCE THEORIES AND A NEW CLASS OF FREE OPERATIONS

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000). 9 SUPPLEMENTAL INFORMATION FOR “A UNIFIED APPROACH TO QUANTUM RESOURCE THEORIES AND A NEW CLASS OF FREE OPERATIONS” I. PROOF OF THEOREMS A. Theorem 1 Here ...

    2000

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