arxiv: 2604.23504 · v1 · submitted 2026-04-26 · 🪐 quant-ph

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Quantum average correlations and complementarity relations via metric-adjusted skew information

Xiaoyu Ma , Qing-Hua Zhang , Cong Xu

Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:19 UTC · model grok-4.3

classification 🪐 quant-ph

keywords average quantum correlationsmetric-adjusted skew informationcomplementarity relationswave-particle featuresmutually unbiased basestwirling channelsquantum entropy

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The pith

Multiple averaging procedures for quantum correlations all produce the same intrinsic quantity independent of the scheme, which then features in complementarity relations with wave and particle aspects measured using metric-adjusted skew in

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

The paper examines how to define average correlations in quantum systems by considering multiple ways to average over bases or channels. It finds that four distinct methods—using mutually unbiased bases, all orthonormal bases, operator bases, and twirling channels—all result in identical expressions for the average correlation. This shows the quantity is scheme-independent and intrinsic to the state. The authors then use metric-adjusted skew information to quantify wave and particle aspects of quantum systems and derive inequalities relating these to the average correlation and quantum entropy. This framework unifies the study of correlations and complementarity in quantum mechanics.

Core claim

All listed averaging procedures lead to the same closed expression for the average correlation, identifying it as an intrinsic quantity. Defining wave and particle features via metric-adjusted skew information then yields complementarity relations among wave and particle features, quantum entropy, and this average correlation.

What carries the argument

Metric-adjusted skew information, serving as the basis for both the average correlation measure and the wave-particle feature quantifiers that enable the complementarity relations.

If this is right

The average correlation qualifies as a scheme-independent property of quantum states.
Complementarity relations connect wave-particle duality, entropy, and correlations through a single information-theoretic quantity.
The framework applies uniformly to different basis choices and group actions in quantum mechanics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This independence suggests the average correlation could serve as a robust resource quantifier in quantum information tasks.
The approach might extend to other measures of nonclassicality or to multipartite systems.
Experimental verification could involve preparing states and measuring in varied bases to confirm the same correlation value.

Load-bearing premise

The metric-adjusted skew information must provide physically valid and meaningful quantifiers for wave and particle features, while the four averaging procedures must be sufficiently representative to imply independence from any reasonable averaging method.

What would settle it

Computing the average correlation for a simple two-qubit state using both the mutually unbiased bases method and the twirling channel method and finding numerically different results would falsify the claim of scheme-independence.

read the original abstract

We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information. Several natural averaging procedures are considered, including complete families of mutually unbiased bases, all orthonormal bases, operator orthonormal bases, and twirling channels induced by the unitary group. All these approaches lead to the same closed expression, which identifies the resulting average correlation as an intrinsic quantity independent of the averaging scheme. By defining measures of wave and particle features via metric-adjusted skew information, we establish complementarity relations among wave and particle features, quantum entropy, and average correlation. These results provide a unified framework for investigating quantum average correlations and complementarity relations in terms of metric-adjusted skew information.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Four specific averaging schemes collapse to the same closed-form average correlation via metric-adjusted skew information, with complementarity relations following from that.

read the letter

The main point is that this paper checks four averaging procedures—complete MUB families, all orthonormal bases, operator orthonormal bases, and unitary twirling—and reports that each produces the identical closed expression for average correlation when built from metric-adjusted skew information. They then define wave and particle features with the same quantity and obtain complementarity relations tying those features to quantum entropy and the average correlation. The agreement across the four cases is the concrete new element, and it lets them present the correlation measure as independent of the particular averaging choice among those methods. That consistency is useful if you already work with skew information for resource quantification in quantum information. The calculations are presented as direct and parameter-free, which keeps the results reproducible in principle. The complementarity relations follow straightforwardly once the definitions are fixed, so the framework hangs together internally. The soft spot is that scheme-independence is shown only by explicit computation on these four procedures. No general theorem is supplied showing that an arbitrary averaging over bases or channels must reproduce the same expression, so the intrinsic claim holds for the listed cases but does not automatically extend further. Defining wave and particle features from the skew information itself also makes the resulting relations somewhat internal to the setup rather than an independent physical constraint. The abstract gives no formulas, so the derivations themselves need to be inspected in the full text to confirm there are no hidden choices. This work sits squarely in quantum information theory for readers already using skew information or complementarity bounds. A specialist in that corner could extract the unified expression for their own calculations. I would send it to peer review. The specific agreement across the four schemes is narrow enough to be checked by a referee, and the relations are worth verifying even if the generality stays limited to the cases shown.

Referee Report

2 major / 1 minor

Summary. The paper claims that four distinct averaging procedures over quantum bases and channels—complete families of mutually unbiased bases, all orthonormal bases, operator orthonormal bases, and unitary twirling channels—all produce the identical closed-form expression for average correlation when computed via metric-adjusted skew information. This common expression is presented as an intrinsic, scheme-independent quantity. The authors then define wave and particle features using the same skew-information measures and derive complementarity relations linking these features to quantum entropy and the average correlation.

Significance. If the explicit calculations for the four schemes are correct and the resulting expression is indeed scheme-independent within the considered class, the work supplies a unified, information-theoretic treatment of average correlations and complementarity that could connect skew-information-based measures to established quantum-information quantities. The absence of free parameters in the final expression and the explicit verification across multiple averaging methods would be strengths, but the significance is limited by the lack of a general argument extending beyond the four cases.

major comments (2)

[Abstract / main derivation sections] Abstract and main text (no numbered section provided): the central claim that the four listed averaging procedures establish full scheme-independence rests only on explicit verification for those specific cases; no general theorem is supplied showing that an arbitrary averaging measure on bases or channels must reproduce the same closed expression. This is load-bearing for the assertion that the quantity is 'intrinsic' and independent of the averaging scheme.
[Complementarity relations section] The complementarity relations derived from the wave/particle measures (defined via metric-adjusted skew information) and the average correlation rely on the closed expression obtained above; any qualification of the scheme-independence claim therefore propagates directly to the strength of the complementarity statements.

minor comments (1)

[Preliminaries] Notation for the metric-adjusted skew information and the averaging operators should be introduced with explicit definitions and consistency checks against standard references (e.g., Wigner-Yanase or other skew-information literature) to aid readability.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We address each of the major comments in detail below and outline the revisions we will make to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract / main derivation sections] Abstract and main text (no numbered section provided): the central claim that the four listed averaging procedures establish full scheme-independence rests only on explicit verification for those specific cases; no general theorem is supplied showing that an arbitrary averaging measure on bases or channels must reproduce the same closed expression. This is load-bearing for the assertion that the quantity is 'intrinsic' and independent of the averaging scheme.

Authors: We appreciate the referee's observation regarding the scope of our scheme-independence claim. Our manuscript demonstrates through explicit calculations that four distinct averaging procedures—complete families of mutually unbiased bases, all orthonormal bases, operator orthonormal bases, and unitary twirling channels—yield the identical closed-form expression for the average correlation using metric-adjusted skew information. These procedures are chosen as they cover key classes of bases and channels commonly used in quantum information theory. While this agreement strongly indicates that the expression is intrinsic and independent of the specific scheme within this representative set, we concur that a general theorem applicable to any conceivable averaging measure is not established. In the revised version, we will modify the abstract and relevant sections to clarify that the scheme-independence is verified for these natural and comprehensive averaging procedures, rather than claiming full generality. We will also include a brief remark suggesting the exploration of a more general proof as a potential avenue for future research. This adjustment ensures the claim is accurately supported by the presented evidence. revision: partial
Referee: [Complementarity relations section] The complementarity relations derived from the wave/particle measures (defined via metric-adjusted skew information) and the average correlation rely on the closed expression obtained above; any qualification of the scheme-independence claim therefore propagates directly to the strength of the complementarity statements.

Authors: We agree with the referee that the complementarity relations are derived using the average correlation expression obtained from the averaging procedures. Consequently, the qualification we will introduce regarding the scheme-independence will be consistently applied to the complementarity statements in the revised manuscript. Specifically, we will state that the relations hold for the average correlation as defined via the considered schemes. This ensures the logical consistency of the results without altering the core derivations. revision: partial

standing simulated objections not resolved

Providing a general theorem establishing scheme-independence for arbitrary averaging measures on bases or channels

Circularity Check

0 steps flagged

No circularity; explicit calculations for listed schemes yield matching expression

full rationale

The paper explicitly computes the average correlation for four concrete averaging procedures (complete families of MUBs, all orthonormal bases, operator orthonormal bases, and unitary twirling) and reports that each produces the identical closed-form expression. This matching result is then used to define the quantity as scheme-independent within the considered cases and to derive complementarity relations with wave/particle measures based on metric-adjusted skew information. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation chain; the coincidence is presented as an outcome of the calculations rather than an input assumption. The derivation remains self-contained against the enumerated methods and external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The framework implicitly assumes metric-adjusted skew information is a suitable quantifier and that the listed averaging schemes suffice.

pith-pipeline@v0.9.0 · 5397 in / 1168 out tokens · 36320 ms · 2026-05-08T06:19:18.398768+00:00 · methodology

discussion (0)

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Works this paper leans on

45 extracted references · 21 canonical work pages

[1]

Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009Rev. Mod. Phys.81(2) 865–942 URLhttps:// link.aps.org/doi/10.1103/RevModPhys.81.865

work page doi:10.1103/revmodphys.81.865
[2]

Modi K, Brodutch A, Cable H, Paterek T and Vedral V 2012Rev. Mod. Phys.84(4) 1655–1707 URLhttps: //link.aps.org/doi/10.1103/RevModPhys.84.1655

work page doi:10.1103/revmodphys.84.1655
[3]

Braun D, Adesso G, Benatti F, Floreanini R, Marzolino U, Mitchell M W and Pirandola S 2018Rev. Mod. Phys. 90035006 URLhttps://link.aps.org/doi/10.1103/ RevModPhys.90.035006
[4]

Datta A, Shaji A and Caves C M 2008Phys. Rev. Lett. 100050502 URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.100.050502
[5]

Phys.8666–670 URLhttps: //doi.org/10.1038/nphys2377

Daki´ c B, Lipp Y O, Ma X, Ringbauer M, Kropatschek S, Barz S, Paterek T, Vedral V, Zeilinger A, Brukner ˇC and Walther P 2012Nat. Phys.8666–670 URLhttps: //doi.org/10.1038/nphys2377

work page doi:10.1038/nphys2377
[6]

Ollivier H and Zurek W H 2001Phys. Rev. Lett. 88017901 URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.88.017901
[7]

Henderson L and Vedral V 2001Journal of Physics A: Mathematical and General346899–6905 URLhttps: //doi.org/10.1088/0305-4470/34/35/315

work page doi:10.1088/0305-4470/34/35/315
[8]

Luo S, Fu S and Oh C H 2012Phys. Rev. A 85(3) 032117 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.85.032117
[9]

Girolami D, Tufarelli T and Adesso G 2013Phys. Rev. Lett.110240402 URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.110.240402
[10]

Girolami D 2014Phys. Rev. Lett.113170401 URL https://link.aps.org/doi/10.1103/PhysRevLett. 113.170401

work page doi:10.1103/physrevlett
[11]

Yu C s 2017Phys. Rev. A95042337 URLhttps:// link.aps.org/doi/10.1103/PhysRevA.95.042337

work page doi:10.1103/physreva.95.042337
[13]

Li L, Wang Q W, Shen S Q and Li M 2021Phys. Rev. A 103012401 URLhttps://link.aps.org/doi/10.1103/ PhysRevA.103.012401
[14]

Sun Y, Li N and Luo S 2023Phys. Rev. A 108062416 URLhttps://link.aps.org/doi/10.1103/ PhysRevA.108.062416
[15]

Tang L and Wu F 2025Phys. Rev. A112(3) 032437 URL https://link.aps.org/doi/10.1103/wwjf-lh44

work page doi:10.1103/wwjf-lh44
[16]

Fan Y, Li N and Luo S 2023Phys. Rev. A 108(5) 052406 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.108.052406
[17]

Process.2471 URL https://doi.org/10.1007/s11128-025-04691-z

Fan Y and Li L 2025Quantum Inf. Process.2471 URL https://doi.org/10.1007/s11128-025-04691-z

work page doi:10.1007/s11128-025-04691-z
[18]

Ma J, Yadin B, Girolami D, Vedral V and Gu M 2016 Phys. Rev. Lett.116(16) 160407 URLhttps://link. aps.org/doi/10.1103/PhysRevLett.116.160407

work page doi:10.1103/physrevlett.116.160407 2016
[21]

Bagan E, Bergou J A, Cottrell S S and Hillery M 2016 Phys. Rev. Lett.116(16) 160406 URLhttps://link. aps.org/doi/10.1103/PhysRevLett.116.160406

work page doi:10.1103/physrevlett.116.160406 2016
[22]

China Phys

Jin Z X, Yang L M, Fei S M, Li-Jost X, Wang Z X, Long G L and Qiao C F 2021Sci. China Phys. Mech. Astron.64280311 URLhttps://doi.org/10.1007/ s11433-021-1709-9
[23]

Streltsov A, Singh U, Dhar H S, Bera M N and Adesso G 2015Phys. Rev. Lett.115(2) 020403 URLhttps:// link.aps.org/doi/10.1103/PhysRevLett.115.020403

work page doi:10.1103/physrevlett.115.020403
[24]

Luo S and Sun Y 2019Phys. Lett. A3832869– 2873 URLhttps://www.sciencedirect.com/science/ article/pii/S0375960119305638
[25]

Lett.11860007 URLhttps://doi.org/10.1209/0295-5075/118/60007

Sun Y, Mao Y and Luo S 2017Europhys. Lett.11860007 URLhttps://doi.org/10.1209/0295-5075/118/60007

work page doi:10.1209/0295-5075/118/60007
[26]

Zhang Q H and Fei S M 2024J. Phys. A: Math. Theor. 57235301 URLhttps://doi.org/10.1088/1751-8121/ ad4aa4

work page doi:10.1088/1751-8121/
[27]

Cheng S and Hall M J W 2015Phys. Rev. A 92(4) 042101 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.92.042101
[28]

Sun L, Tao Y H and Fei S M 2022Laser Physics 33015204 URLhttps://doi.org/10.1088/1555-6611/ aca4cc

work page doi:10.1088/1555-6611/
[29]

Che X J, Tao Y H, Sheng Y H, Wu S H and Fei S M 2023Results Phys.52106794 URL https://www.sciencedirect.com/science/article/ pii/S2211379723005879
[30]

Rep.762-7641–100 URL https://www.sciencedirect.com/science/article/ pii/S0370157318301893

Hu M L, Hu X, Wang J, Peng Y, Zhang Y R and Fan H 2018Phys. Rep.762-7641–100 URL https://www.sciencedirect.com/science/article/ pii/S0370157318301893
[31]

Rastegin A E 2016Phys. Rev. A93(3) 032136 10 URLhttps://link.aps.org/doi/10.1103/PhysRevA. 93.032136

work page doi:10.1103/physreva
[32]

Coles P J 2016Phys. Rev. A93(6) 062111 URLhttps: //link.aps.org/doi/10.1103/PhysRevA.93.062111

work page doi:10.1103/physreva.93.062111
[33]

Yang K K, Wang Z X and Fei S M 2024Phys. Rev. A110(4) 042413 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.110.042413
[34]

Wang X and Fu S 2025Phys. Rev. A112(1) 012222 URL https://link.aps.org/doi/10.1103/wdxh-nwsw

work page doi:10.1103/wdxh-nwsw
[35]

Hansen F 2008Proc. Natl. Acad. Sci. U. S. A.105 9909–9916 ISSN 0027-8424 URLhttps://www.pnas. org/content/105/29/9909
[36]

Cai L and Hansen F 2010Lett. Math. Phys.931–13 URL https://doi.org/10.1007/s11005-010-0396-2

work page doi:10.1007/s11005-010-0396-2
[37]

Gibilisco P, Girolami D and Hansen F 2021Entropy-switz 23263 URLhttps://doi.org/10.3390/e23030263

work page doi:10.3390/e23030263
[38]

Fan Y J, Yang X Y and Li L L 2024Mod. Phys. Lett. A392450174 URLhttps://doi.org/10.1142/ S0217732324501748
[39]

Sha X, Fan Y and Yang Y 2026Int. J. Theor. Phys.6573 URLhttps://doi.org/10.1007/s10773-025-06248-3

work page doi:10.1007/s10773-025-06248-3
[40]

Li N, Zhang Z, Luo S and Sun Y 2024Phys. Rev. A110(2) 022418 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.110.022418
[41]

Sun Y, Li N and Luo S 2022Phys. Rev. A 106(1) 012436 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.106.012436
[42]

Gibilisco P, Hansen F and Isola T 2009Linear Al- gebra Appl.4302225–2232 ISSN 0024-3795 URL https://www.sciencedirect.com/science/article/ pii/S0024379508005648
[43]

Furuichi S and Yanagi K 2012J. Math. Anal. Appl.3881147–1156 ISSN 0022-247X URL https://www.sciencedirect.com/science/article/ pii/S0022247X11010183
[44]

Gibilisco P, Imparato D and Isola T 2007J. Math. Phys. 48072109 ISSN 0022-2488 URLhttps://doi.org/10. 1063/1.2748210
[45]

Gibilisco P, Imparato D and Isola T 2009Proc. Amer. Math. Soc.137317–327 URLhttps://doi.org/10. 1090/S0002-9939-08-09447-1
[46]

Gibilisco P and Isola T 2011J. Math. Anal. Appl.375270–275 ISSN 0022-247X URL https://www.sciencedirect.com/science/article/ pii/S0022247X10007730
[47]

Li N, Luo S and Sun Y 2022Phys. Rev. A 105(3) 032436 URLhttps://link.aps.org/doi/10. 1103/PhysRevA.105.032436
[48]

Zhang L 2014arXiv preprint arXiv:1408.3782URL https://arxiv.org/abs/1408.3782

work page arXiv