Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z
Paper Citation Record · LEDGER
Sufficiency and Petz recovery for positive maps
As of 20 August 2026, this Paper Citation Record lists 90 of 90 outbound references and 3 inbound Pith citation observations for arXiv:2604.08380.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-12T17:42:54.732991Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T02:26:42.781926Z
Reference resolution
90 of 90 outbound references displayed
- verified exact49
- verified fuzzy24
- unresolved5
- parse uncertain0
- malformed identifier11
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 0003fb4b-c543-47a0-acc6-529c573533bb · outbound
This paper cites Detection Theory and Quantum Mechanics.
Sufficiency and Petz recovery for positive maps Detection Theory and Quantum Mechanics
Reference 1
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.231073Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1ad16d15-b73d-4797-be70-f6dddc62e110 · outbound
This paper cites Strong Converse an d Stein’s Lemma in Quantum Hypothesis Testing.
Sufficiency and Petz recovery for positive maps Strong Converse an d Stein’s Lemma in Quantum Hypothesis Testing
Reference 2
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.382356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0773c544-fe2f-42b9-bb8a-616d14fa5687 · outbound
This paper cites Tomamichel.
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.388146Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b21cb873-b2f5-4572-b168-bd3145e93236 · outbound
This paper cites Quantum Information Processing with Finite Resources.
Sufficiency and Petz recovery for positive maps Quantum Information Processing with Finite Resources
Reference 4
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.210289Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8bb8c7ef-d3e0-4f12-8902-fdce3439651e · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 5
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.301119Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ddf26104-cb8a-45fe-8f1e-6b5caefa1598 · outbound
This paper cites A Problem Relating to Positive Linear Maps on Matrix Algebras.
Sufficiency and Petz recovery for positive maps A Problem Relating to Positive Linear Maps on Matrix Algebras
Reference 6
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.201606Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d5100d55-d7cc-436d-855f-bd35819f5ed5 · outbound
This paper cites Matsumoto.
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.490420Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e9e77b6d-b78d-401c-aae2-1aae773de70e · outbound
This paper cites Extending quantum operations.
Sufficiency and Petz recovery for positive maps Extending quantum operations
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-05-15T06:45:09.874721Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 07310367-3bcc-4f9e-b9ea-b06836e762ec · outbound
This paper cites Comparison of Quantum Statistical Models: Equivalent Conditions forSufficiency.
Sufficiency and Petz recovery for positive maps Comparison of Quantum Statistical Models: Equivalent Conditions forSufficiency
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.431495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 37c5ecdd-f019-40f5-b6c6-8b050dbcc821 · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 10
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.242619Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ad09b93d-0427-4513-a1f2-65907abf8caa · outbound
This paper cites Quantum Relative Lorenz Curves.
Sufficiency and Petz recovery for positive maps Quantum Relative Lorenz Curves
Reference 11
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.215812Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 870bca7a-08cb-47a6-b6d7-469fb21b3f9c · outbound
This paper cites Quantum majorization and a complete set of entropic conditions for quantum thermodynamics , url =.
Sufficiency and Petz recovery for positive maps Quantum majorization and a complete set of entropic conditions for quantum thermodynamics , url =
Reference 12
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.270103Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fbe44023-6c9f-4291-91cd-41dfab4e0825 · outbound
This paper cites An information-theoretic treatment of quantum dichotomies.
Sufficiency and Petz recovery for positive maps An information-theoretic treatment of quantum dichotomies
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.473445Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 18527656-c1c0-47db-84e4-3d63d03c658d · 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.
Sufficiency and Petz recovery for positive maps An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map
Reference 14
- Resolution
- verified exact
- local_arxiv, observed 2026-05-15T06:45:10.833099Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6446398c-1b3b-40ca-99f2-94748834ecc2 · outbound
This paper cites Sufficiency of Rényi Divergences.
Sufficiency and Petz recovery for positive maps Sufficiency of Rényi Divergences
Reference 15
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.310520Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 27bf1d44-f97c-41a9-8878-f7f74331c610 · outbound
This paper cites α-z-Rényi Relative Entropies.
Sufficiency and Petz recovery for positive maps α-z-Rényi Relative Entropies
Reference 16
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.191456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8ea1436b-7cc7-4b0a-8078-dd4e126a1943 · outbound
This paper cites On α-z-Rényi Divergence in the von Neumann Algebra Setting.
Sufficiency and Petz recovery for positive maps On α-z-Rényi Divergence in the von Neumann Algebra Setting
Reference 17
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.290729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ffb4deaa-ec89-4a3e-8cba-584e70e018b2 · outbound
This paper cites Hiai and A.
Reference 18
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.315038Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 472036ad-3c61-4442-acd5-4e84b1e03956 · outbound
This paper cites Quasi-Entropies for States of a von Neumann Algebra.
Sufficiency and Petz recovery for positive maps Quasi-Entropies for States of a von Neumann Algebra
Reference 19
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.360822Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6c60c772-f70d-4c49-91f4-edce67f44808 · outbound
This paper cites Quasi-Entropies for Finite Quantum Systems.
Sufficiency and Petz recovery for positive maps Quasi-Entropies for Finite Quantum Systems
Reference 20
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.296445Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 53b6ce18-593a-451b-9acc-a296c367fca0 · outbound
This paper cites Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Rela- tive Entropy.
Sufficiency and Petz recovery for positive maps Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Rela- tive Entropy
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.469676Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c1ed9417-38cf-4711-916a-0c175c497597 · outbound
This paper cites Wilde, Andreas Winter, and Dong Yang.
Sufficiency and Petz recovery for positive maps Wilde, Andreas Winter, and Dong Yang
Reference 22
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.411743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 882f05fd-40de-4f41-bf44-bbcd8558227c · outbound
This paper cites On quan- tum Rényi entropies: A new generalization and some properti es.
Sufficiency and Petz recovery for positive maps On quan- tum Rényi entropies: A new generalization and some properti es
Reference 23
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.394520Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4ebe05e3-f2da-406a-8633-241f1e84b44f · outbound
This paper cites The Journal of Chemical Physics 132(21), 214102 (2010).
Sufficiency and Petz recovery for positive maps The Journal of Chemical Physics 132(21), 214102 (2010)
Reference 24
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.366583Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f0d595b9-a6f6-44bc-a085-900beb689ef7 · outbound
This paper cites Rényi Divergences as Weighted Non- commutative Vector-ValuedLp-Spaces.
Sufficiency and Petz recovery for positive maps Rényi Divergences as Weighted Non- commutative Vector-ValuedLp-Spaces
Reference 25
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.174994Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2c1d9492-4364-40f8-91d6-fe3e4d82ea1f · outbound
This paper cites Monotonicity of the Quantum Relative Entropy Under Positive Maps.
Sufficiency and Petz recovery for positive maps Monotonicity of the Quantum Relative Entropy Under Positive Maps
Reference 27
- Resolution
- verified exact
- local_arxiv, observed 2026-05-15T06:45:10.400845Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5153bb75-b555-4b8f-a382-1a1e06bf315d · outbound
This paper cites Integral formula for quantum relative entropy implies data process- ing inequality.
Sufficiency and Petz recovery for positive maps Integral formula for quantum relative entropy implies data process- ing inequality
Reference 28
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.442989Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ac38ab1e-f78c-42ea-afb6-7c85aa3af822 · outbound
This paper cites Ohya and D.
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.461675Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6b0f355e-3423-41cf-9c7f-a258c1815fd2 · outbound
This paper cites Sufficiencyin quantum statistical inference: a surveywith examples.
Sufficiency and Petz recovery for positive maps Sufficiencyin quantum statistical inference: a surveywith examples
Reference 30
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.325266Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bc076874-b7e4-4a3c-ae0a-58e0392147ba · outbound
This paper cites Minimal sufficient statistical experiments on von Neumann alge- bras.
Sufficiency and Petz recovery for positive maps Minimal sufficient statistical experiments on von Neumann alge- bras
Reference 31
- Resolution
- malformed identifier
- raw_fallback, observed 2026-05-15T06:45:12.410418Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 892e1222-b3d5-4df5-9f38-73935d084768 · outbound
This paper cites Operations that do not disturb quantum states.
Sufficiency and Petz recovery for positive maps Operations that do not disturb quantum states
Reference 32
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.390556Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e0439713-8c8a-4b75-8244-43724989ff69 · outbound
This paper cites Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality.
Sufficiency and Petz recovery for positive maps Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
Reference 33
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.405835Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 93dd39b0-d8e3-45b0-89a9-7fd84d99a3a8 · outbound
This paper cites Sufficient subalgebras and the relative entropy of states of a von Neu- mannalgebra.
Sufficiency and Petz recovery for positive maps Sufficient subalgebras and the relative entropy of states of a von Neu- mannalgebra
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.487120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ecc3538c-606e-436e-96f7-ccd91f824d7a · outbound
This paper cites Sufficient subalgebras and the relative entropy of states of a von neumann algebra.
Sufficiency and Petz recovery for positive maps Sufficient subalgebras and the relative entropy of states of a von neumann algebra
Reference 35
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.305935Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1253b9aa-c7a1-4adc-a032-140cd925bf7b · outbound
This paper cites Sufficiency of channels over von Neumann algebras.
Sufficiency and Petz recovery for positive maps Sufficiency of channels over von Neumann algebras
Reference 36
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.320466Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation edde8a81-4203-403c-91e8-4ab9c7c38317 · outbound
This paper cites Sonoda, H.
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.465532Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 74904eee-4c6d-45bb-b4a6-a57f17ca042d · outbound
This paper cites Hypothesis testing and Stein's lemma in general probability theories with Euclidean Jordan algebra and its quantum realization.
Sufficiency and Petz recovery for positive maps Hypothesis testing and Stein's lemma in general probability theories with Euclidean Jordan algebra and its quantum realization
Reference 38
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:09.883791Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b1c7acc2-b4ad-4d7f-b6fd-b80d1261c692 · outbound
This paper cites C∗-Algebraic Generalization of Relative En- tropy and Entropy.
Sufficiency and Petz recovery for positive maps C∗-Algebraic Generalization of Relative En- tropy and Entropy
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.493906Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a5b320e3-76c5-4e24-8989-b93dbfc6ac86 · outbound
This paper cites Quantum Hypothesis Testing and Sufficient Subalgebras.
Sufficiency and Petz recovery for positive maps Quantum Hypothesis Testing and Sufficient Subalgebras
Reference 40
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.334385Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9088ebf7-72d2-4dc7-a6ec-01ff7dedb541 · outbound
This paper cites Layer Cake Representations for Quantum Divergences.
Sufficiency and Petz recovery for positive maps Layer Cake Representations for Quantum Divergences
Reference 41
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.251750Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9d5ea891-4745-4a83-9007-deabeac183c7 · outbound
This paper cites Quantum Differential Privacy: An Information Theory Perspective.
Sufficiency and Petz recovery for positive maps Quantum Differential Privacy: An Information Theory Perspective
Reference 42
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.259981Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e09f89cf-bbb6-469f-9b22-99acaa66ad6b · outbound
This paper cites Quantum Rényi andf-divergences from inte- gral representations.
Sufficiency and Petz recovery for positive maps Quantum Rényi andf-divergences from inte- gral representations
Reference 43
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.353657Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation af856c96-2f4a-44a0-844b-e27fad34162f · outbound
This paper cites Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem.
Sufficiency and Petz recovery for positive maps Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem
Reference 44
- Resolution
- verified exact
- arxiv_id, observed 2026-06-05T02:16:18.626304Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 21398b46-e0fd-4842-995e-1edf2a2cafef · outbound
This paper cites Cheng, G.
Reference 45
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.846016Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6c948707-759d-41b5-a4bb-362c06eb1697 · outbound
This paper cites Preservation of a Quantum Rényi Relative Entropy Implies Existence of a Recovery Map.
Sufficiency and Petz recovery for positive maps Preservation of a Quantum Rényi Relative Entropy Implies Existence of a Recovery Map
Reference 46
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.447682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3c507e99-4d22-4634-afb7-f1928d5d77d3 · outbound
This paper cites Rényi Relative Entropies and NoncommutativeLp-Spaces.
Sufficiency and Petz recovery for positive maps Rényi Relative Entropies and NoncommutativeLp-Spaces
Reference 47
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.458191Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8f1e9fa8-4c22-44aa-88e2-0f44b3d9ca1b · outbound
This paper cites Rényi Relative Entropies and NoncommutativeLp-Spaces II.
Sufficiency and Petz recovery for positive maps Rényi Relative Entropies and NoncommutativeLp-Spaces II
Reference 48
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.428248Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d9e0cd96-4bfb-4d96-ba9b-8f91a255bc68 · outbound
This paper cites Hanche-Olsen and E.
Sufficiency and Petz recovery for positive maps Hanche-Olsen and E
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.438793Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 03f946c0-fec3-4f44-8ace-9ef627a42524 · outbound
This paper cites Recoverability of quantum channels via hypothesis testing.
Sufficiency and Petz recovery for positive maps Recoverability of quantum channels via hypothesis testing
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.454187Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9e3bd779-e1ac-487e-9fef-3e220a565744 · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 51
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T06:45:12.504825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6b7fae17-8ed1-4549-8270-ed15f6deef1f · outbound
This paper cites Quantum Conditional Mutual Information and Approxi- mate Markov Chains.
Sufficiency and Petz recovery for positive maps Quantum Conditional Mutual Information and Approxi- mate Markov Chains
Reference 52
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.371425Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3478ed58-7378-4992-9abc-d7f663dbc2d3 · outbound
This paper cites Recoverability in Quantum Information Theory.
Sufficiency and Petz recovery for positive maps Recoverability in Quantum Information Theory
Reference 53
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:09.906480Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5669b2c3-5fda-4df2-832c-5d61955e8056 · outbound
This paper cites Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map.
Sufficiency and Petz recovery for positive maps Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
Reference 54
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.378780Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d1297192-a33e-46de-be47-92fb12977a33 · outbound
This paper cites Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy.
Sufficiency and Petz recovery for positive maps Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy
Reference 55
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.433409Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 367061c7-d51b-42ad-8c20-41dc241e212b · outbound
This paper cites Approximate recovery and relative entropy I. general von Neumann subalgebras.
Sufficiency and Petz recovery for positive maps Approximate recovery and relative entropy I. general von Neumann subalgebras
Reference 56
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.839324Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2f55b800-9080-48f0-8b49-8dd523767030 · outbound
This paper cites Approximate Recoverability and Relative Entropy II: 2-Positive Channels of General von Neumann Algebras.
Sufficiency and Petz recovery for positive maps Approximate Recoverability and Relative Entropy II: 2-Positive Channels of General von Neumann Algebras
Reference 57
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.285988Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 7e91f8b4-d077-45c4-b719-b09c14ebd2ae · outbound
This paper cites Positive linear maps of operator algebras.
Sufficiency and Petz recovery for positive maps Positive linear maps of operator algebras
Reference 58
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.236905Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 45f78043-b1f6-4c45-8a56-0ea9b733bc34 · outbound
This paper cites Multiplicative Properties of Positive Maps.
Sufficiency and Petz recovery for positive maps Multiplicative Properties of Positive Maps
Reference 59
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.343915Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation dc300c1f-e423-4ca4-a5bc-4a9857416844 · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 60
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T06:45:12.451116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6b617231-13e7-48f4-bb03-af011265310b · outbound
This paper cites Brown and N.
Sufficiency and Petz recovery for positive maps Brown and N
Reference 61
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:09.892214Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 32eb6c70-43d4-4bac-bc5a-c97bb7f15d50 · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 62
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T06:45:12.447577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0b220e5c-80e6-458e-bf70-a293bacd0f14 · outbound
This paper cites Quantum Compression and Fixed Points of Schwarz Maps.
Sufficiency and Petz recovery for positive maps Quantum Compression and Fixed Points of Schwarz Maps
Reference 63
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.384273Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f9fc0c56-ae76-4ddd-8126-282a01d2997c · outbound
This paper cites Selfpolar forms and their applications to the C*-algebra the- ory.
Sufficiency and Petz recovery for positive maps Selfpolar forms and their applications to the C*-algebra the- ory
Reference 64
- Resolution
- malformed identifier
- raw_fallback, observed 2026-05-15T06:45:12.396337Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3a8887c2-1de8-410f-9c27-5c3bd8329290 · outbound
This paper cites Tomita-Takesaki Theory for Jordan Alge- bras.
Sufficiency and Petz recovery for positive maps Tomita-Takesaki Theory for Jordan Alge- bras
Reference 65
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.418576Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c58ac95f-19a2-49b3-82a9-0d0b159a8c22 · outbound
This paper cites Conditional Expectations on Jordan Algebras.
Sufficiency and Petz recovery for positive maps Conditional Expectations on Jordan Algebras
Reference 66
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.264983Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation da321452-f82e-4ae3-b2b0-2fb4b30d483e · outbound
This paper cites quantum holonomy.
Sufficiency and Petz recovery for positive maps quantum holonomy
Reference 67
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.416487Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8cf21e71-7992-4426-9beb-ae7bef46d56e · outbound
This paper cites Some aspects of quantum sufficiency for finite and full von Neumann algebras.
Sufficiency and Petz recovery for positive maps Some aspects of quantum sufficiency for finite and full von Neumann algebras
Reference 68
- Resolution
- malformed identifier
- raw_fallback, observed 2026-05-15T06:45:12.392212Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ed63f360-c0bf-4587-81de-c90af6c294f1 · outbound
This paper cites Conditional Expectations in von Neumann Algebras.
Sufficiency and Petz recovery for positive maps Conditional Expectations in von Neumann Algebras
Reference 69
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.386464Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1cb5a19f-db1d-4728-8bdd-37f1b95d2edc · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 70
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T06:45:12.435222Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation dcc7bb42-0424-42fc-811e-2b1ab6d773ab · outbound
This paper cites The product of projection operators.
Sufficiency and Petz recovery for positive maps The product of projection operators
Reference 71
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.402096Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b78ca367-9915-4e72-a205-4d05c6faeb9b · outbound
This paper cites On an Algebraic Generalization of the Quantum Mechanical Formalism.
Sufficiency and Petz recovery for positive maps On an Algebraic Generalization of the Quantum Mechanical Formalism
Reference 72
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.480398Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bbba1e1f-676a-457c-bb6f-c14ad880bd1e · outbound
This paper cites Jordan, J.
Reference 73
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:09.859628Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 722eefd4-a508-427b-8fa2-ffe5984a9e5a · outbound
This paper cites Jacobson.
Reference 74
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.476937Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 85d4a2f5-2a55-4f9b-b012-869c7c35d233 · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 75
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.184899Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 74e79393-2d4f-411e-acca-2d55ccaf6a62 · outbound
This paper cites On the structure of positive maps.
Sufficiency and Petz recovery for positive maps On the structure of positive maps
Reference 76
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.406413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1af68a87-6ee6-4d20-b0b8-568fba45d39f · outbound
This paper cites Classification and Representation of Semi- Simple Jordan Algebras.
Sufficiency and Petz recovery for positive maps Classification and Representation of Semi- Simple Jordan Algebras
Reference 77
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.281224Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 84f7aabe-4dd0-4151-856f-6e02dbc89cad · outbound
This paper cites Decomposition of Positive Projections on C*-Algebras.
Sufficiency and Petz recovery for positive maps Decomposition of Positive Projections on C*-Algebras
Reference 78
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.422836Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 643cd36c-8847-42bd-8fe6-b3bb2ce5c90d · outbound
This paper cites Nonassociative Lp-spaces and embeddings in noncommutative Lp- spaces.
Sufficiency and Petz recovery for positive maps Nonassociative Lp-spaces and embeddings in noncommutative Lp- spaces
Reference 79
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T06:45:10.225589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 47d046b7-cac5-43db-8ebf-36abe4164670 · outbound
This paper cites Chapter 25 - Quasi-Banach Spaces.
Sufficiency and Petz recovery for positive maps Chapter 25 - Quasi-Banach Spaces
Reference 80
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.483567Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1707b30f-b30c-4487-aad5-4821f8eee5c5 · outbound
This paper cites Quantum Sufficiency in the Operator Algebra Framework.
Sufficiency and Petz recovery for positive maps Quantum Sufficiency in the Operator Algebra Framework
Reference 81
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.497656Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 69368786-0364-4df7-8a0a-fa702a67c800 · outbound
This paper cites PTP-Interconvertibility for Quantum States via the Minimal Suffi- cient Jordan Algebra.
Sufficiency and Petz recovery for positive maps PTP-Interconvertibility for Quantum States via the Minimal Suffi- cient Jordan Algebra
Reference 82
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.443124Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1738b4ad-b9a8-4328-9a3c-47419724efaa · outbound
This paper cites Invariant states for positive operator semigroups.
Sufficiency and Petz recovery for positive maps Invariant states for positive operator semigroups
Reference 83
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.427391Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bbf7e5b0-56fc-4d96-bf38-095938b22b53 · outbound
This paper cites Positive projections onto spin factors.
Sufficiency and Petz recovery for positive maps Positive projections onto spin factors
Reference 84
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.275853Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 663bcbbe-6f9f-45af-9e05-506725353fa4 · outbound
This paper cites Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture.
Sufficiency and Petz recovery for positive maps Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture
Reference 85
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T06:45:12.414676Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d24b4577-0e98-420a-9ec7-24a0837be0b4 · outbound
This paper cites Frank and Elliott H.
Sufficiency and Petz recovery for positive maps Frank and Elliott H
Reference 86
- Resolution
- metadata mismatch
- doi, observed 2026-05-15T06:45:10.330012Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 78857261-e81b-4197-9a83-5cef31662031 · outbound
This paper cites Inequalities for Quantum Divergences and the Audenaert–Datta Conjecture.
Sufficiency and Petz recovery for positive maps Inequalities for Quantum Divergences and the Audenaert–Datta Conjecture
Reference 87
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.437623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 06675ed0-a371-4be9-b5a9-a44a1fa41ae2 · outbound
This paper cites The structure of the inverse system of Gorensteink-algebras.
Sufficiency and Petz recovery for positive maps The structure of the inverse system of Gorensteink-algebras
Reference 88
- Resolution
- malformed identifier
- doi_truncated, observed 2026-05-15T06:45:10.349199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5a06a78a-02de-4a88-93b6-2b753a8ad604 · outbound
This paper cites an unresolved cited work.
Sufficiency and Petz recovery for positive maps Unresolved cited work
Reference 89
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T06:45:12.500916Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 7f52de2e-95a2-468e-bc0e-514214185b77 · outbound
This paper cites Gruppentheorie und ihre Anwen- dung auf die Quantenmechanik der Atomspektren.
Sufficiency and Petz recovery for positive maps Gruppentheorie und ihre Anwen- dung auf die Quantenmechanik der Atomspektren
Reference 90
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.422283Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 606739d2-2234-482d-9dcf-038abf728e2a · outbound
This paper cites Quaternions and matrices of quaternions.
Sufficiency and Petz recovery for positive maps Quaternions and matrices of quaternions
Reference 91
- Resolution
- verified exact
- doi, observed 2026-05-15T06:45:10.339237Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
Observation dd31c328-3ca3-4b90-a98a-88b1ea1471e3 · inbound
Integral representations of $f$-divergences for general von Neumann algebras cites this paper.
Integral representations of $f$-divergences for general von Neumann algebras Sufficiency and Petz recovery for positive maps
Reference 29
- Resolution
- verified exact
- local_arxiv, observed 2026-07-08T00:14:22.326850Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fe698128-9288-445c-a094-c86ba194cb79 · inbound
Hockey stick $f$-divergences cites this paper.
Hockey stick $f$-divergences Sufficiency and Petz recovery for positive maps
Reference 54
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T02:26:42.783304Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1512f051-9c30-476e-86af-765df0e342ca · inbound
Quantum steering is equivalent to state-preserving conditional expectations cites this paper.
Quantum steering is equivalent to state-preserving conditional expectations Sufficiency and Petz recovery for positive maps
Reference 55
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T17:42:54.732991Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.