Paper Citation Record · LEDGER

Quantum Noncommutativity Uniquely Determines Relative Entropy

As of 20 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 1 inbound Pith citation observation for arXiv:2607.01712.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.01712 v2

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:44:19.129707Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:23:31.635899Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-15T15:23:32.666373Z

Reference resolution

55 of 55 outbound references displayed

verified exact0
verified fuzzy6
unresolved48
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

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Outbound references

Observation e4180cb6-9f63-4af4-b55f-69695668f91b · outbound

This paper cites an unresolved cited work.

Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.871612Z

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Observation 6d4a180e-2e25-43dc-91a0-b5349dcdb0d2 · outbound

This paper cites an unresolved cited work.

Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 2

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Observation fd42643b-101f-4ea3-a182-87c2414aed55 · outbound

This paper cites Watrous,The Theory of Quantum Information(Cam- bridge University Press, 2018).

Quantum Noncommutativity Uniquely Determines Relative Entropy Watrous,The Theory of Quantum Information(Cam- bridge University Press, 2018)

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.882758Z

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Observation 7a41de16-6d37-4c1f-a658-40ced2d875dd · outbound

This paper cites Tomamichel,Quantum Information Processing with Finite Resources: Mathematical Foundations, Springer- Briefs in Mathematical Physics (Springer International Publishing, 2015).

Quantum Noncommutativity Uniquely Determines Relative Entropy Tomamichel,Quantum Information Processing with Finite Resources: Mathematical Foundations, Springer- Briefs in Mathematical Physics (Springer International Publishing, 2015)

Reference 4

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Observation 9b4e2e15-0249-4655-a2b7-b71278cb241a · outbound

This paper cites Principles of Quantum Communication Theory: A Modern Approach.

Quantum Noncommutativity Uniquely Determines Relative Entropy Principles of Quantum Communication Theory: A Modern Approach

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.892557Z

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Observation 811b44c3-20b9-4fa6-a953-916a4e35d635 · outbound

This paper cites Gour,Quantum Resource Theories(Cambridge Uni- versity Press, 2025).

Quantum Noncommutativity Uniquely Determines Relative Entropy Gour,Quantum Resource Theories(Cambridge Uni- versity Press, 2025)

Reference 6

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Observation 803df4f8-dcac-4a86-95f7-7d2fadc16155 · outbound

This paper cites Reverse Test and Characterization of Quantum Relative Entropy.

Quantum Noncommutativity Uniquely Determines Relative Entropy Reverse Test and Characterization of Quantum Relative Entropy

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.902678Z

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Observation 49bb4712-d972-4570-99c4-e8402710f6a3 · outbound

This paper cites Wilming, R.

Quantum Noncommutativity Uniquely Determines Relative Entropy Wilming, R

Reference 8

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Observation 5cd69f09-7c11-461f-ae3a-a590229f92d0 · outbound

This paper cites Blackwell, Ann.

Quantum Noncommutativity Uniquely Determines Relative Entropy Blackwell, Ann

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.912161Z

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Observation 40e45f1f-2488-459b-af1e-534bf07c3013 · outbound

This paper cites Shmaya,38, 9717 (2005).

Quantum Noncommutativity Uniquely Determines Relative Entropy Shmaya,38, 9717 (2005)

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.916658Z

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Observation 38eb64c3-d3e4-4e0f-8c3c-c567fe0631e3 · outbound

This paper cites Buscemi, Communications in Mathematical Physics 310, 625 (2012).

Quantum Noncommutativity Uniquely Determines Relative Entropy Buscemi, Communications in Mathematical Physics 310, 625 (2012)

Reference 11

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Observation 38be0086-d6af-4e0e-a5d3-f95078b11cda · outbound

This paper cites Buscemi, N.

Quantum Noncommutativity Uniquely Determines Relative Entropy Buscemi, N

Reference 12

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Observation fd105896-43a1-46f6-a495-260596ab5c23 · outbound

This paper cites A quantum version of randomization criterion.

Quantum Noncommutativity Uniquely Determines Relative Entropy A quantum version of randomization criterion

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.930080Z

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Observation c4872e10-61a3-4abd-b3da-542a8fd371bb · outbound

This paper cites Jencov´ a, in2016 IEEE International Symposium on Information Theory (ISIT)(IEEE, 2016) pp.

Quantum Noncommutativity Uniquely Determines Relative Entropy Jencov´ a, in2016 IEEE International Symposium on Information Theory (ISIT)(IEEE, 2016) pp

Reference 14

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Observation 8b41f106-f350-436f-90a7-610a3e0fab34 · outbound

This paper cites Takagi and B.

Quantum Noncommutativity Uniquely Determines Relative Entropy Takagi and B

Reference 15

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Observation a7f8a3ee-c1e5-4e6c-b233-98bc0bf35789 · outbound

This paper cites Skrzypczyk, I.

Quantum Noncommutativity Uniquely Determines Relative Entropy Skrzypczyk, I

Reference 16

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Observation b776b980-e13d-4146-af8f-a5023cb1f7b3 · outbound

This paper cites Brandsen, I.

Quantum Noncommutativity Uniquely Determines Relative Entropy Brandsen, I

Reference 17

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Observation 354cc853-e005-40be-8938-dd6c24a0329f · outbound

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Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 18

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Observation c86c6915-b72f-4748-805e-db59d0827f0f · outbound

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Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 19

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Observation c97c51ad-7549-4e61-b0db-5fb1dc03c7fc · outbound

This paper cites Buscemi and G.

Quantum Noncommutativity Uniquely Determines Relative Entropy Buscemi and G

Reference 20

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Observation 09c9a14f-ace1-46aa-8e9f-b1760f0bb3fa · outbound

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Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 21

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Observation cde92f9a-cd41-470c-a269-cb2917eceb1d · outbound

This paper cites Wang and R.

Quantum Noncommutativity Uniquely Determines Relative Entropy Wang and R

Reference 22

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Observation c18bf2cd-5d5b-49e0-8604-bf2fea9e0eb5 · outbound

This paper cites Buscemi and N.

Quantum Noncommutativity Uniquely Determines Relative Entropy Buscemi and N

Reference 23

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Observation 59b1ee93-ccaa-42dc-b061-aed5cba6a368 · outbound

This paper cites Nagaoka and M.

Quantum Noncommutativity Uniquely Determines Relative Entropy Nagaoka and M

Reference 24

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Observation 6ce0f629-60c0-4805-a03b-59b22020ed6d · outbound

This paper cites Datta and R.

Quantum Noncommutativity Uniquely Determines Relative Entropy Datta and R

Reference 25

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Observation c60b1e27-702d-4070-9901-77f656500b8b · outbound

This paper cites Tomamichel and M.

Quantum Noncommutativity Uniquely Determines Relative Entropy Tomamichel and M

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.991006Z

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Observation 7c253b21-d335-4eb0-a6dc-14a68f565a8b · outbound

This paper cites Datta, IEEE Transactions on Information Theory55, 2816 (2009).

Quantum Noncommutativity Uniquely Determines Relative Entropy Datta, IEEE Transactions on Information Theory55, 2816 (2009)

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.995335Z

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Observation f3552756-c231-4989-8e53-82bdc67ca064 · outbound

This paper cites Datta, M.

Quantum Noncommutativity Uniquely Determines Relative Entropy Datta, M

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:18.999792Z

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Observation aca7ef76-c327-4b8d-a114-aa7798a7229b · outbound

This paper cites Datta and F.

Quantum Noncommutativity Uniquely Determines Relative Entropy Datta and F

Reference 29

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Observation bffd930e-ba14-44cf-a58d-dfd076eab450 · outbound

This paper cites Hirche and M.

Quantum Noncommutativity Uniquely Determines Relative Entropy Hirche and M

Reference 30

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Observation 9a4db895-53c4-41b4-b262-896240d25cac · outbound

This paper cites Sason and S.

Quantum Noncommutativity Uniquely Determines Relative Entropy Sason and S

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:44:19.669240Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 17969673-03b5-42bb-aa7c-a14dd17c0bd0 · outbound

This paper cites Layer Cake Representations for Quantum Divergences.

Quantum Noncommutativity Uniquely Determines Relative Entropy Layer Cake Representations for Quantum Divergences

Reference 32

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Observation 96c4ea0f-1d5c-4f39-9470-dbd1d8638c54 · outbound

This paper cites Sharp estimates of quantum covering problems via a novel trace inequality.

Quantum Noncommutativity Uniquely Determines Relative Entropy Sharp estimates of quantum covering problems via a novel trace inequality

Reference 33

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Observation 8a3c3763-8968-406c-878a-e4cc3b807bcb · outbound

This paper cites Cheng, G.

Quantum Noncommutativity Uniquely Determines Relative Entropy Cheng, G

Reference 34

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Observation 63ee214d-b092-4bad-9602-db30d0c258b1 · outbound

This paper cites Berta, H.-C.

Quantum Noncommutativity Uniquely Determines Relative Entropy Berta, H.-C

Reference 35

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Observation 5a784a35-b99d-4eef-8516-e4d5d3209445 · outbound

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Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 36

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Observation 1a0cd954-a9f4-457f-934e-505e72cba9a5 · outbound

This paper cites Arthur F.

Quantum Noncommutativity Uniquely Determines Relative Entropy Arthur F

Reference 37

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Observation 5e6687f9-e8a0-4c1a-9e01-5f5f0de5493d · outbound

This paper cites Oppenheim and M.

Quantum Noncommutativity Uniquely Determines Relative Entropy Oppenheim and M

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:19.045701Z

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Observation c2eaaab6-633a-425e-9483-8b0a1eea9fbf · outbound

This paper cites Dahl, Linear Algebra and its Applications288, 53 (1999).

Quantum Noncommutativity Uniquely Determines Relative Entropy Dahl, Linear Algebra and its Applications288, 53 (1999)

Reference 39

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Observation 318cf57c-e381-4ba3-88d7-fffd5daeba4d · outbound

This paper cites Alberti and A.

Quantum Noncommutativity Uniquely Determines Relative Entropy Alberti and A

Reference 40

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Observation 924f8b03-6007-4ab0-a80a-097eb4051f80 · outbound

This paper cites Dall’Arno, F.

Quantum Noncommutativity Uniquely Determines Relative Entropy Dall’Arno, F

Reference 41

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Observation cf6011b2-9665-4c87-bda2-897fb610311c · outbound

This paper cites An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map.

Quantum Noncommutativity Uniquely Determines Relative Entropy An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:19.064348Z

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Observation c8f8945b-2226-4fae-9279-27035ed51727 · outbound

This paper cites Shaked and J.

Quantum Noncommutativity Uniquely Determines Relative Entropy Shaked and J

Reference 43

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Observation 2f5e4308-2925-4bd5-85d8-b633d81a856f · outbound

This paper cites Gour and M.

Quantum Noncommutativity Uniquely Determines Relative Entropy Gour and M

Reference 44

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Observation 86a4b561-b2b2-4b1a-af3b-01851101bb65 · outbound

This paper cites Binomial Approximation to Locally Dependent CDO.

Quantum Noncommutativity Uniquely Determines Relative Entropy Binomial Approximation to Locally Dependent CDO

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:19.078843Z

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Observation f49e569d-dacd-4a3a-8c27-ee6ca7bac7c1 · outbound

This paper cites Denuit, J.

Quantum Noncommutativity Uniquely Determines Relative Entropy Denuit, J

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:19.083992Z

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Observation 5c66c071-3079-48be-aeb0-7333fa964249 · outbound

This paper cites Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem.

Quantum Noncommutativity Uniquely Determines Relative Entropy Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-15T15:44:19.089401Z

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Observation fb91cbe9-1d7a-4406-9aeb-702b3df5baf6 · outbound

This paper cites These are the usual pure-state projectors, or equivalently the sharp yes/no measurements associated with directions on the Bloch sphere.

Quantum Noncommutativity Uniquely Determines Relative Entropy These are the usual pure-state projectors, or equivalently the sharp yes/no measurements associated with directions on the Bloch sphere

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:44:19.577088Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 631fe69b-315b-4561-be5b-242a9607f7e2 · outbound

This paper cites more ellipses.

Quantum Noncommutativity Uniquely Determines Relative Entropy more ellipses

Reference 49

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:44:19.561646Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation eb4be3d9-61ad-45f8-9440-621456a40863 · outbound

This paper cites Furthermore,a α(s)⩾0 and lim s↑1 aα(s) = α2 2(2−α) .(S15).

Quantum Noncommutativity Uniquely Determines Relative Entropy Furthermore,a α(s)⩾0 and lim s↑1 aα(s) = α2 2(2−α) .(S15)

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:44:19.546508Z

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Observation 8ec72da8-5275-4190-8e8c-560860e66cd5 · outbound

This paper cites an unresolved cited work.

Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:44:19.530176Z

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Observation d19e7be5-9f93-455d-b4ee-58a06ed8a351 · outbound

This paper cites 1− s2γp s2γ2 +r 2 # .(S25) Substitution into (S22) gives Qα(ρr∥σs) =γ α − + α 2 Z γ+ γ− γα−1.

Quantum Noncommutativity Uniquely Determines Relative Entropy 1− s2γp s2γ2 +r 2 # .(S25) Substitution into (S22) gives Qα(ρr∥σs) =γ α − + α 2 Z γ+ γ− γα−1

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:44:19.513401Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e83e010b-8fb1-450d-98c6-108063f8798a · outbound

This paper cites an unresolved cited work.

Quantum Noncommutativity Uniquely Determines Relative Entropy Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:44:19.497870Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9bfe323a-f49f-4a40-bc89-80a891989195 · outbound

This paper cites To prove the upper bound, letEbe the pinching channel in the eigenbasis ofσ s, which satisfiesE(ρ r) =ρ 0 andE(σ s) =σ s.

Quantum Noncommutativity Uniquely Determines Relative Entropy To prove the upper bound, letEbe the pinching channel in the eigenbasis ofσ s, which satisfiesE(ρ r) =ρ 0 andE(σ s) =σ s

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:44:19.482768Z

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Observation 9ef76eb0-0c1e-4ca3-ae6c-23efc1a585d7 · outbound

This paper cites For the second part, recall the definitionb α(s) :=S α(s)−L α(s).

Quantum Noncommutativity Uniquely Determines Relative Entropy For the second part, recall the definitionb α(s) :=S α(s)−L α(s)

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:44:19.466773Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation d7c2401d-bad2-45d5-b4eb-ee8c949f9552 · inbound

Maximal R\'enyi Relative Entropy for $\alpha>2$ cites this paper.

Maximal R\'enyi Relative Entropy for $\alpha>2$ Quantum Noncommutativity Uniquely Determines Relative Entropy

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:23:32.740602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.