Paper Citation Record · LEDGER

Alternating minimization for computing doubly minimized Petz Renyi mutual information

As of 9 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 1 inbound Pith citation observation for arXiv:2507.05205.

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pith.paper-citation-record.v1
2507.05205 v1

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measured 56 of 56 reference resolution

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: pith, observed 2026-08-08T15:46:29.229680Z

Reference resolution

56 of 56 outbound references displayed

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verified fuzzy18
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External citation measurements

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Outbound references

Observation 52b9cb9b-132f-45f7-81ac-c7e07244c666 · outbound

This paper cites an unresolved cited work.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:41:02.366203Z

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Observation 4fa73c5b-3270-4335-947d-357164673291 · outbound

This paper cites Notation We take “log” to refer to the natural logarithm.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Notation We take “log” to refer to the natural logarithm

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.352259Z

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Observation deeaa437-77c5-4f98-aaf9-cc546445b4cc · outbound

This paper cites The following definition formalizes the alternating minimization problem under consideration.

Alternating minimization for computing doubly minimized Petz Renyi mutual information The following definition formalizes the alternating minimization problem under consideration

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.338592Z

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Observation d3d2c2f8-7695-4bc1-976b-14d5013a8f61 · outbound

This paper cites Our main results address the non-asymptotic convergence of the objective function values after n iterations of alternating minimization, denoted byxn.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Our main results address the non-asymptotic convergence of the objective function values after n iterations of alternating minimization, denoted byxn

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.324883Z

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Observation a294b55e-a57c-489a-88fd-47d231ce0727 · outbound

This paper cites Probability mass functions Let X be a finite set.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Probability mass functions Let X be a finite set

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.310354Z

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Observation 76ebebd9-3ef0-475f-aac9-eb71b00d3af1 · outbound

This paper cites 12 Definition 2(Alternating minimization: Iteration rule).

Alternating minimization for computing doubly minimized Petz Renyi mutual information 12 Definition 2(Alternating minimization: Iteration rule)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.294930Z

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Observation 6ade059a-3c73-466b-aa5a-16b479635454 · outbound

This paper cites Let α ∈ (0, 1) ∪ (1, ∞) and let Q, R ∈ P(X ) be such that Q ∼ R.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Let α ∈ (0, 1) ∪ (1, ∞) and let Q, R ∈ P(X ) be such that Q ∼ R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.280650Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b783163a-9a95-4644-8bce-29f488f64972 · outbound

This paper cites (A.36) follows from the additivity of Hilbert’s projective metric with respect to the product of PMFs.

Alternating minimization for computing doubly minimized Petz Renyi mutual information (A.36) follows from the additivity of Hilbert’s projective metric with respect to the product of PMFs

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.265140Z

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Observation 77e8d43f-c534-45ea-84e8-7a7cac15c6f7 · outbound

This paper cites All of the following hold.

Alternating minimization for computing doubly minimized Petz Renyi mutual information All of the following hold

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.251184Z

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Observation 49c6761f-4739-416c-8842-46b7576e5ae0 · outbound

This paper cites By the fixed-point property of minimizers for the doubly minimized PRMI [17], ˆσA = NB→A ◦ NA→B(ˆσA) ∈ S≪ρA(A), (C.14) ˆτB = NA→B(ˆσA) ∈ S≪ρB (B).

Alternating minimization for computing doubly minimized Petz Renyi mutual information By the fixed-point property of minimizers for the doubly minimized PRMI [17], ˆσA = NB→A ◦ NA→B(ˆσA) ∈ S≪ρA(A), (C.14) ˆτB = NA→B(ˆσA) ∈ S≪ρB (B)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.236768Z

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Observation f8e44178-f7b4-4729-9025-7e856004e147 · outbound

This paper cites Let α ∈ (1, ∞) and let σ, τ∈ S(A) be such thatσ ∼ τ.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Let α ∈ (1, ∞) and let σ, τ∈ S(A) be such thatσ ∼ τ

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.221517Z

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Observation 7eb5cc90-fd34-4ec2-90a3-e497ab7827ea · outbound

This paper cites Let σ, τ∈ S(A) be such that σ ∼ τ.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Let σ, τ∈ S(A) be such that σ ∼ τ

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.207313Z

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Observation 29ba6373-6193-4839-abac-c041ce275573 · outbound

This paper cites Let α ∈ ( 1 2 , 1), ρAB ∈ S(AB), σ(0) A ∈ S∼ρA(A).

Alternating minimization for computing doubly minimized Petz Renyi mutual information Let α ∈ ( 1 2 , 1), ρAB ∈ S(AB), σ(0) A ∈ S∼ρA(A)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.192526Z

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Observation 504bb9f0-4f9f-4b14-9c2e-0ef1af924006 · outbound

This paper cites Before presenting the proof, we first clarify our notation for Fréchet derivatives.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Before presenting the proof, we first clarify our notation for Fréchet derivatives

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.179050Z

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Observation 2440d87e-d867-4630-9ac6-e1a6a6430f5f · outbound

This paper cites Decomposition rules for quantum Rényi mutual infor- mation with an application to information exclusion relations.Journal of Mathematical Physics, 61(7),.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Decomposition rules for quantum Rényi mutual infor- mation with an application to information exclusion relations.Journal of Mathematical Physics, 61(7),

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.164040Z

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Observation 94c677b3-8f0a-4084-bde9-73c15bb88a4d · outbound

This paper cites an unresolved cited work.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.504407Z

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Observation d4eb97ed-4342-41ff-9835-7863ea110d45 · outbound

This paper cites Sandwiched Rényi divergence satisfies data processing inequality.Journal of Mathemat- ical Physics, 54(12), 2013.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Sandwiched Rényi divergence satisfies data processing inequality.Journal of Mathemat- ical Physics, 54(12), 2013

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:58.654075Z

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Observation b771fc3a-55da-4150-b1c7-c1fc4778324b · outbound

This paper cites Wilde, and Nilanjana Datta.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Wilde, and Nilanjana Datta

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:58.716418Z

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Observation f57a2d37-e895-4f83-9d93-7c071314d9a3 · outbound

This paper cites Tight One-Shot Analysis for Convex Splitting with Applications in Quantum Information Theory.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Tight One-Shot Analysis for Convex Splitting with Applications in Quantum Information Theory

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:58.777146Z

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Observation 9fa71da2-4bb4-4047-921f-f79ea356dec0 · outbound

This paper cites Wilde, Andreas Winter, and Dong Yang.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Wilde, Andreas Winter, and Dong Yang

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:58.831078Z

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Observation 346d9b4f-a54b-4693-bd79-0f54de37fbd7 · outbound

This paper cites Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence

Reference 21

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.794830Z

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Observation 5137c2c8-2830-4589-8206-47140c959dcf · outbound

This paper cites Operational Interpretation of the Sandwiched Rényi Divergence of Order 1/2 to 1 as Strong Converse Exponents.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Operational Interpretation of the Sandwiched Rényi Divergence of Order 1/2 to 1 as Strong Converse Exponents

Reference 22

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.781378Z

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Observation 24429dee-b9dc-4735-b62c-722fbb285175 · outbound

This paper cites Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.033990Z

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Observation 5446efe2-d5c6-4a0b-98fb-8f59d0c3ad35 · outbound

This paper cites Gupta and Mark M.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Gupta and Mark M

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.084980Z

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Observation 00a611a9-1d15-4bf2-97c2-99ca1c62c8f0 · outbound

This paper cites Seshadreesan, and Mark M.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Seshadreesan, and Mark M

Reference 25

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.742297Z

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Observation c94fb572-0dea-4fbc-9e66-46e743adb0f3 · outbound

This paper cites Coding Theorems for Compound Problems via Quantum Rényi Divergences.IEEE Transactions on Information Theory, 61(6):2997–3012, 2015.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Coding Theorems for Compound Problems via Quantum Rényi Divergences.IEEE Transactions on Information Theory, 61(6):2997–3012, 2015

Reference 26

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Observation c71320ed-dfcc-4b7e-8c11-367eb3406139 · outbound

This paper cites Strong Converse Exponent for Classical-Quantum Channel Coding.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Strong Converse Exponent for Classical-Quantum Channel Coding

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.262949Z

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Observation 3668e94e-4091-4431-98e8-337b0d62cb42 · outbound

This paper cites Correlation detection and an operational interpre- tation of the Rényi mutual information.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Correlation detection and an operational interpre- tation of the Rényi mutual information

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.333205Z

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Unavailable: canonical work link unavailable.

Observation 1a17cb3a-c46c-4d01-8be4-8d071092bcd0 · outbound

This paper cites Rényi mutual information in quantum field theory, tensor networks, and gravity.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Rényi mutual information in quantum field theory, tensor networks, and gravity

Reference 29

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.709344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6d6145a5-4a12-4966-a30c-2e3a2916c83e · outbound

This paper cites Rényi Mutual Information in Quantum Field Theory.Physical Review Letters, 130(021603), 2023.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Rényi Mutual Information in Quantum Field Theory.Physical Review Letters, 130(021603), 2023

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.453810Z

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Observation 3514be62-a5ba-4f09-904c-6eb510c603df · outbound

This paper cites Zaslavski.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Zaslavski

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.107049Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ad5c7a5e-591d-4d2f-afd0-4e751289bfa7 · outbound

This paper cites Doubly minimized Petz and sandwiched Renyi mutual information: Properties.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Doubly minimized Petz and sandwiched Renyi mutual information: Properties

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.540960Z

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Observation 226a18ef-b534-4d9d-8a2c-fd270a9975e1 · outbound

This paper cites an unresolved cited work.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 33

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Observation 58cc5bb1-f863-488d-be61-a4291b989618 · outbound

This paper cites Two Measures of Dependence.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Two Measures of Dependence

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T19:40:59.763727Z

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Observation f529028f-ac11-4e63-a095-d881eaf38b1f · outbound

This paper cites Min-reflected entropy = doubly minimized Petz Rényi mutual information of order 1/2,.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Min-reflected entropy = doubly minimized Petz Rényi mutual information of order 1/2,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.148361Z

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Observation 07e96cf4-5454-457e-94fb-cbd96c593485 · outbound

This paper cites Positive Definite Matrices.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Positive Definite Matrices

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.394155Z

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Observation 6269307c-a0dc-41c8-94d3-91b59ee04c67 · outbound

This paper cites Alternating Optimization Approach for Computing $\alpha$-Mutual Information and $\alpha$-Capacity.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Alternating Optimization Approach for Computing $\alpha$-Mutual Information and $\alpha$-Capacity

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:41:01.625750Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e19bd9da-67f1-4388-a293-0bc9305bf3ae · outbound

This paper cites Linear Convergence in Hilbert’s Projective Metric for Computing Augustin Information and a Rényi Information Measure,.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Linear Convergence in Hilbert’s Projective Metric for Computing Augustin Information and a Rényi Information Measure,

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.134663Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3e135871-e602-4774-8608-6e21016050e4 · outbound

This paper cites On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces.

Alternating minimization for computing doubly minimized Petz Renyi mutual information On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces

Reference 40

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.585693Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bd0cf9b7-d019-46e2-9014-d2d8ed77dac0 · outbound

This paper cites Quasi-entropies for finite quantum systems.Reports on Mathematical Physics, 23(1):57–65,.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Quasi-entropies for finite quantum systems.Reports on Mathematical Physics, 23(1):57–65,

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:41:02.120566Z

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Observation 85767fba-2d7e-4d15-8706-9907eb7034e1 · outbound

This paper cites an unresolved cited work.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 43

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.561919Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9c1005e7-4abb-46d8-a023-87f2e9e017ad · outbound

This paper cites Cambridge Tracts in Math- ematics.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Cambridge Tracts in Math- ematics

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:00.855264Z

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Observation 3b4e85c0-fd24-4a95-8040-a98fc2650994 · outbound

This paper cites Birkhoff's version of Hilbert's metric and its applications in analysis.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Birkhoff's version of Hilbert's metric and its applications in analysis

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:41:01.538382Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1680fff0-7bc3-4055-a5ab-119a29e52a61 · outbound

This paper cites Kastoryano, and Michael M.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Kastoryano, and Michael M

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.044551Z

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Observation 340d5bc5-8ae9-43fa-824f-a091088471d3 · outbound

This paper cites Bauschke and Patrick L.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Bauschke and Patrick L

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.145245Z

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Unavailable: canonical work link unavailable.

Observation 4027bec7-a8fc-4fd4-af84-771e0c083585 · outbound

This paper cites Zaslavski.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Zaslavski

Reference 48

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.498321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ed427a0a-f58a-47e3-8ea2-1a40ab8183d9 · outbound

This paper cites Quantum Information Processing with Finite Resources.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Quantum Information Processing with Finite Resources

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.377055Z

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Observation 368b2ff1-fb3f-499f-9735-1f577242d856 · outbound

This paper cites Extensions of Jentzsch’s Theorem.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Extensions of Jentzsch’s Theorem

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.380975Z

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Observation 09f12033-31df-46f6-b332-7517ecf3fbdc · outbound

This paper cites An Inequality for Positive Linear Integral Operators.

Alternating minimization for computing doubly minimized Petz Renyi mutual information An Inequality for Positive Linear Integral Operators

Reference 53

Resolution: verified exact; raw_fallback, observed 2026-08-06T19:41:01.932623Z

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Observation 1913e580-e1d2-4cf5-95ed-239dbbf406ee · outbound

This paper cites On the Convergence of Block Coordinate Descent Type Methods.

Alternating minimization for computing doubly minimized Petz Renyi mutual information On the Convergence of Block Coordinate Descent Type Methods

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.389902Z

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Observation c82db811-5b66-4ba9-9dcf-4200386b65ab · outbound

This paper cites Matrix Analysis.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Matrix Analysis

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-06T19:41:01.398121Z

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Observation 51a50f43-fa18-4c44-820b-83d0b77b3969 · outbound

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Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 1986

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Observation 4dec37dc-8d1e-4584-a4d6-99de51f558e7 · outbound

This paper cites an unresolved cited work.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 2020

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This paper cites an unresolved cited work.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Unresolved cited work

Reference 2022

Resolution: verified exact; doi, observed 2026-08-06T19:41:01.484220Z

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Observation f2b499a0-d4c9-43d5-bf68-d65b514ab3f1 · outbound

This paper cites Linear Convergence in Hilbert's Projective Metric for Computing Augustin Information and a R\'{e}nyi Information Measure.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Linear Convergence in Hilbert's Projective Metric for Computing Augustin Information and a R\'{e}nyi Information Measure

Reference 2024

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Observation 7d96e6ad-aa67-41d6-aa4b-71c0a1bba9d4 · outbound

This paper cites Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2.

Alternating minimization for computing doubly minimized Petz Renyi mutual information Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2

Reference 2025

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Pith citing papers

Observation c9f42eed-8126-45cc-a5a2-6cbac0690296 · inbound

A Linearly Convergent Algorithm for Computing the Petz-Augustin Mean cites this paper.

A Linearly Convergent Algorithm for Computing the Petz-Augustin Mean Alternating minimization for computing doubly minimized Petz Renyi mutual information

Reference 10

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