Complete Quantum Relational Hoare Logics from Optimal Transport Duality | Paper Citation Record

Observation d8a94c4a-588a-4c37-bde2-928f888ef015 · outbound

This paper cites Quantum relational hoare logic,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum relational hoare logic,

Reference 1

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Observation 1512fd1d-6f8b-43a8-9ea7-020f7b2c7342 · outbound

This paper cites Relational proofs for quantum programs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Relational proofs for quantum programs,

Reference 2

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Observation 3e7f5276-60a3-4fcc-a61a-4def2dfb1994 · outbound

This paper cites Quantum Relational Hoare Logic with E x- pectations,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum Relational Hoare Logic with E x- pectations,

Reference 3

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Observation d2004561-3843-4a6c-aa37-4d53efed307d · outbound

This paper cites A quantitative probabilistic relational hoare logic,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A quantitative probabilistic relational hoare logic,

Reference 4

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Observation c6ce977a-5da4-4b8c-93e5-d48c53575af9 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 5

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Observation 796a4a75-f3e7-4005-bf57-ac58614d4f63 · outbound

This paper cites The existence of probability measures wit h given marginals,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality The existence of probability measures wit h given marginals,

Reference 6

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Observation 0747d5ce-846a-44ed-afb5-c7a7b8358b0f · outbound

This paper cites Strassen’s theorem for quantum couplings,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Strassen’s theorem for quantum couplings,

Reference 7

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Observation b62c8709-513b-4243-ae32-7e0d4c803bd4 · outbound

This paper cites On quantum optimal transport,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality On quantum optimal transport,

Reference 8

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Observation a8579c8e-b0a4-4dd0-99d9-70f37cf94c1c · outbound

This paper cites M´ emoire sur la th´ eorie des d´ eblais et des re mblais,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality M´ emoire sur la th´ eorie des d´ eblais et des re mblais,

Reference 9

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Observation b4234245-6aa7-4477-a404-5760d4ccff19 · outbound

This paper cites Monotonicity of a quantum 2-wasserstein distance,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Monotonicity of a quantum 2-wasserstein distance,

Reference 10

Resolution: verified exact; doi, observed 2026-08-10T14:36:23.638434Z

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Observation fb87bc45-7b2f-4452-9f26-b40299c30eae · outbound

This paper cites On the monotonicity of a quantum optimal transport cost.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality On the monotonicity of a quantum optimal transport cost

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.310280Z

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Observation 4495a5a7-f79e-47ae-ad6b-d1664729a76d · outbound

This paper cites Quantum earth mover ’s distance, a no-go quantum Kantorovich–Rubinstein theorem, and quant um marginal problem,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum earth mover ’s distance, a no-go quantum Kantorovich–Rubinstein theorem, and quant um marginal problem,

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.313826Z

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Observation c2d11b29-d8e1-4f01-af58-2a036d221806 · outbound

This paper cites Monogamy of quantum entanglem ent and other correlations,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Monogamy of quantum entanglem ent and other correlations,

Reference 13

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Observation e6043cc3-35d5-4af7-965f-fb91a38aca4a · outbound

This paper cites Floyd–hoare logic for quantum programs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Floyd–hoare logic for quantum programs,

Reference 14

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Observation e9394c13-59d1-428d-b323-7d89ecb1460d · outbound

This paper cites San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 2016.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 2016

Reference 15

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Observation 94073545-d129-46e2-b1d0-8e076fc0022b · outbound

This paper cites Approximate relational rea soning for quan- tum programs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Approximate relational rea soning for quan- tum programs,

Reference 16

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Observation 44218d3c-0c8e-4de5-b049-fbcb4b0c6c92 · outbound

This paper cites An applied quantum hoare log ic,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality An applied quantum hoare log ic,

Reference 17

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Observation aa4350dc-5cb1-407c-8240-27213c73b903 · outbound

This paper cites Quantitative robustness analysis of quantum programs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantitative robustness analysis of quantum programs,

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.332369Z

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Observation e3ecd361-043b-42ee-83c2-67a5a31d514b · outbound

This paper cites Glei pnir: toward practical error analysis for quantum programs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Glei pnir: toward practical error analysis for quantum programs,

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.335389Z

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Observation a87996ff-d1c8-4426-82a7-0ae1b7e04718 · outbound

This paper cites Quantum Computing in the NISQ era and beyo nd,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum Computing in the NISQ era and beyo nd,

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.338426Z

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Observation 0df8fa9a-1661-4e07-a587-9ebed5ece8d3 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.340887Z

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Observation 32973b43-27b6-4266-a680-eeb14aa53100 · outbound

This paper cites Quantum circuits with mixed states,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum circuits with mixed states,

Reference 22

Resolution: metadata mismatch; raw_fallback, observed 2026-08-10T14:36:23.870778Z

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Observation 20cde2b2-203f-4c0a-9fc7-51456e500a08 · outbound

This paper cites Quantum information-ﬂow se curity: Noninterference and access control,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum information-ﬂow se curity: Noninterference and access control,

Reference 23

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Observation 28efce47-c160-4b58-ba7a-fd59572d5677 · outbound

This paper cites Gentle measurement of q uantum states and differential privacy,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Gentle measurement of q uantum states and differential privacy,

Reference 24

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Observation 9ee9e412-7517-43a9-bf8e-c933b1ad7265 · outbound

This paper cites Differential privacy in quantum co mputation,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Differential privacy in quantum co mputation,

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.351994Z

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Observation d0d59fe9-0c33-4d05-a4d1-ca6dbb3dc67b · outbound

This paper cites For mal certiﬁcation of code-based cryptographic proofs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality For mal certiﬁcation of code-based cryptographic proofs,

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.355124Z

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Observation 765229c2-f91c-44ff-92a2-1b5e042f3bb4 · outbound

This paper cites A pre-expectation calculus for probabilistic sensitivity,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A pre-expectation calculus for probabilistic sensitivity,

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.357472Z

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Observation f390ce37-0d5b-4040-bbe2-24e8e75357d8 · outbound

This paper cites Asynchronous probabilistic couplings in hig her-order separation logic,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Asynchronous probabilistic couplings in hig her-order separation logic,

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.359780Z

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Observation efaa719d-21e7-4e12-96d2-f7fe38400d0f · outbound

This paper cites The monge distance between quantum states,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality The monge distance between quantum states,

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.362547Z

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Observation 9998540e-4a38-40e8-b58a-c17394bcced8 · outbound

This paper cites The monge metric on the sphere and geometry of quantum states,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality The monge metric on the sphere and geometry of quantum states,

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.365728Z

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Observation 5652d983-e7e0-4d63-bace-2a1d1f24292b · outbound

This paper cites On the mean ﬁeld and cla ssical limits of quantum mechanics,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality On the mean ﬁeld and cla ssical limits of quantum mechanics,

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.368981Z

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Observation 99d45942-1e1f-4157-9a04-1d0d711f8124 · outbound

This paper cites Quantum and Semiquantum Pseudome trics and applications,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum and Semiquantum Pseudome trics and applications,

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.372530Z

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Observation cfecd730-5217-4eb3-a39e-40b48e9b4b5d · outbound

This paper cites To- wards Optimal Transport for Quantum Densities,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality To- wards Optimal Transport for Quantum Densities,

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.376091Z

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Observation a50c7b0a-d934-4d38-9f21-605b0b1bb63a · outbound

This paper cites Quantum optimal transport is cheaper,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum optimal transport is cheaper,

Reference 34

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Observation edac704d-2fdf-43de-a815-aa69fb9bcda1 · outbound

This paper cites Quantum optimal transport with quantum channels,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum optimal transport with quantum channels,

Reference 35

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Observation 85ef1594-29cc-499a-a032-9ea0de3909d8 · outbound

This paper cites Cham: Springer Nature Switzerland, 2024, pp.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Cham: Springer Nature Switzerland, 2024, pp

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.389436Z

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Observation 610cf6b0-52c6-463f-9ae5-9d19f4031cbe · outbound

This paper cites Li mitations of variational quantum algorithms: A quantum optimal trans port approach,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Li mitations of variational quantum algorithms: A quantum optimal trans port approach,

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.392902Z

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Observation 990f5a62-2882-4b04-a780-2a26708103dc · outbound

This paper cites Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.395691Z

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Observation ec056194-d85c-4677-ba92-e7dfc6bdc069 · outbound

This paper cites Quantum monge-kantorovich problem and transport distance between density matrices,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum monge-kantorovich problem and transport distance between density matrices,

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.342260Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 829a30c3-428a-4539-96ca-9d7c7052cf87 · outbound

This paper cites Quantum earth mover ’s distance, a no-go quantum kantorovich–rubinstein theorem , and quantum marginal problem,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum earth mover ’s distance, a no-go quantum kantorovich–rubinstein theorem , and quantum marginal problem,

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.335376Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4f28657f-ac8f-4c5a-90c8-ba4cfe8f25f8 · outbound

This paper cites A categorical semantics of quantum protocols.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A categorical semantics of quantum protocols

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.403734Z

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Observation 92c405e4-ccd6-47bc-8a0a-6a01f6be86c9 · outbound

This paper cites Coecke and A.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Coecke and A

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.327818Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 079c5b35-d5e9-4ad8-8dde-05af10c7ef57 · outbound

This paper cites Heunen and J.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Heunen and J

Reference 43

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Observation 5e32629a-f16a-4f26-9669-5585dc810bc9 · outbound

This paper cites Interacting quantum observab les,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Interacting quantum observab les,

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.319771Z

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Observation 8fa0c31d-b714-4e4f-afe0-bb0680feeb40 · outbound

This paper cites Zh: A complete graphical c alculus for quantum computations involving classical non-lineari ty,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Zh: A complete graphical c alculus for quantum computations involving classical non-lineari ty,

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.311827Z

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Observation 59c2e192-a07c-43e9-831c-a3ac1d040ab6 · outbound

This paper cites A Diagrammatic Axiomatisation for Qubit Entanglement.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A Diagrammatic Axiomatisation for Qubit Entanglement

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.421938Z

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Observation 201fd846-ee39-4987-95e0-d9b9998c4be1 · outbound

This paper cites Automating equational pr oofs in dirac notation,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Automating equational pr oofs in dirac notation,

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.425388Z

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Observation 10aed373-8ec1-4e01-9c48-215200e92544 · outbound

This paper cites Algebraic effects, linearity, and quantum programming languages,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Algebraic effects, linearity, and quantum programming languages,

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.427852Z

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Observation d21a9cbf-573a-44c8-b6de-f1a89c08b8a1 · outbound

This paper cites Wit h a few square roots, quantum computing is as easy as pi,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Wit h a few square roots, quantum computing is as easy as pi,

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.303885Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 94af87b4-3ad2-4dba-889b-25e73aee5e3e · outbound

This paper cites A Process Algebraic Approach to Concurrent and Distributed Quantum Computation: Operational Semantics.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A Process Algebraic Approach to Concurrent and Distributed Quantum Computation: Operational Semantics

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.434978Z

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Observation 0cb2165e-c985-485c-b9ed-1920b766d903 · outbound

This paper cites Communicating Quantum Processes.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Communicating Quantum Processes

Reference 51

Resolution: verified exact; local_arxiv, observed 2026-08-10T14:36:23.667921Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bd105e51-9a71-40f1-b137-a3ea55c5aba1 · outbound

This paper cites Quantum bisimilarity via barbs and contexts: Curbing the power of no n- deterministic observers,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Quantum bisimilarity via barbs and contexts: Curbing the power of no n- deterministic observers,

Reference 52

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T14:36:24.296389Z

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Observation 847cf297-2fd5-4b23-8a39-fd428746430b · outbound

This paper cites An Algebra of Quantum Processes.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality An Algebra of Quantum Processes

Reference 53

Resolution: verified exact; local_arxiv, observed 2026-08-10T14:36:23.657915Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d1d7cc9c-cbba-4525-8e57-b0276f49c804 · outbound

This paper cites Relationa l proofs for quantum programs,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Relationa l proofs for quantum programs,

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.289924Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 69a36e27-6b8f-4348-97f5-a0e28127bdd9 · outbound

This paper cites Introduction to Haar Measure Tools in Quant um Informa- tion: A Beginner’s Tutorial,.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Introduction to Haar Measure Tools in Quant um Informa- tion: A Beginner’s Tutorial,

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.283284Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 00b7bc6c-c518-4506-a35d-25156a72c792 · outbound

This paper cites N OTATIONS AND PRELIMINARIES.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality N OTATIONS AND PRELIMINARIES

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.276430Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 38c8c28c-bf93-4c11-8b57-125eab6d56c5 · outbound

This paper cites If ǫ = +∞, then both (1) and (2) trivially hold.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality If ǫ = +∞, then both (1) and (2) trivially hold

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.269628Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7d19dc55-cdcb-4ae7-8752-6c47c44c2fca · outbound

This paper cites • For any A ∈ Pos(H1 ⊗ H2), we deﬁne A⋆ ∈ Pos(H⋆ 1 ⊗ H⋆.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality • For any A ∈ Pos(H1 ⊗ H2), we deﬁne A⋆ ∈ Pos(H⋆ 1 ⊗ H⋆

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.263120Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d485b80c-3a45-4cc0-8fc5-a48b42b5f1c3 · outbound

This paper cites • For ρ ∈ D(H⋆ 1 ⊗ H⋆ 2), we deﬁne the projection: Π ⊥ ⋆ (ρ) = (P ⊥ ⋆ ⊗P ⊥ ⋆ )ρ(P ⊥ ⋆ ⊗P ⊥ ⋆ ) ∈ D(H1 ⊗ H2).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality • For ρ ∈ D(H⋆ 1 ⊗ H⋆ 2), we deﬁne the projection: Π ⊥ ⋆ (ρ) = (P ⊥ ⋆ ⊗P ⊥ ⋆ )ρ(P ⊥ ⋆ ⊗P ⊥ ⋆ ) ∈ D(H1 ⊗ H2)

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.255772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8e56d3b6-7b2e-4d94-bb6f-8c6e8da72419 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 63

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.249111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation dbcef39d-aa92-48e7-9397-b60ba73e170c · outbound

This paper cites In fact, Π ⊥ ⋆ (ρ↑) = ρ.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality In fact, Π ⊥ ⋆ (ρ↑) = ρ

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.242972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 000264b2-e3e1-4704-9b94-e34ad3999522 · outbound

This paper cites As a consequence, if ρ : ⟨ρ1,ρ 2⟩p, then tr(A⋆ρ↑) = tr(Aρ).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality As a consequence, if ρ : ⟨ρ1,ρ 2⟩p, then tr(A⋆ρ↑) = tr(Aρ)

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.236506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d0e93f4d-639d-4302-8b10-8338b555a595 · outbound

This paper cites Π ⊥ ⋆ (ρ↑) = ρ is trivial by computation.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Π ⊥ ⋆ (ρ↑) = ρ is trivial by computation

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.229010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 26df3132-018b-4a12-8962-4d7669d76923 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.222688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 374c6704-b071-4e3f-aeeb-1419848aae96 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 68

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.216602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 515cd10c-0fc4-45b3-9e58-e4d0a398e4d1 · outbound

This paper cites • (1 ⇒ 3).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality • (1 ⇒ 3)

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.209122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b9ed9caf-401f-49bb-8e14-93d582f27297 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 70

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.203084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation da328780-9646-40bb-b055-8a6b31b8d2b8 · outbound

This paper cites What remaining to be shown is (2) equivalent to (4).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality What remaining to be shown is (2) equivalent to (4)

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.196609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 162c0f46-4cbd-4cbb-a870-91bca7045193 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 72

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.190062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 103d100c-3c0c-400c-8165-fe9f0606955d · outbound

This paper cites • (2 ⇒ 4).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality • (2 ⇒ 4)

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.183479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d6c1e162-2a34-41df-ba23-89c503cd5cc2 · outbound

This paper cites Furthermore, observe that tr(Z1ρ⋆.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Furthermore, observe that tr(Z1ρ⋆

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.176757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 649ea253-95be-4a7d-b80a-96f9c17f11b9 · outbound

This paper cites Q UANTUM OPTIMAL TRANSPORT.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Q UANTUM OPTIMAL TRANSPORT

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.169493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4d4ca7ba-41c0-482f-9785-212ebdd38c10 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 77

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.156221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation effc8a4f-1a5c-4d9a-b89e-a8a507433741 · outbound

This paper cites On the other hand, 1 + tr(cσ) = 1 −c +c(1 + tr(σ)) ≥ 1 −c +c(tr(E1(ρ′ 1/c)) + tr(E2(ρ′ 2/c))) = 1 −c + (tr(E1(ρ′ 1)) + tr(E2(ρ′ 2))).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality On the other hand, 1 + tr(cσ) = 1 −c +c(1 + tr(σ)) ≥ 1 −c +c(tr(E1(ρ′ 1/c)) + tr(E2(ρ′ 2/c))) = 1 −c + (tr(E1(ρ′ 1)) + tr(E2(ρ′ 2)))

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.150159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation eb4fd9d0-6078-48b3-a67d-78857456c641 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 79

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.141484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 50020edd-4353-4791-b9b1-efe773671353 · outbound

This paper cites Lemma C.4 (Monotonicity for Quantum Channels).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Lemma C.4 (Monotonicity for Quantum Channels)

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.134005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5327faca-d21d-4adf-862f-604879c68355 · outbound

This paper cites (E1, E2) is monotone w.r .t.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality (E1, E2) is monotone w.r .t

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.126852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0f0219b0-df0d-4ba5-a35a-d0004d855d72 · outbound

This paper cites Suppose (E1, E2) is monotone w.r .t.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Suppose (E1, E2) is monotone w.r .t

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.119494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 46fc821b-f09d-40cf-9d3a-9983bfc32725 · outbound

This paper cites Suppose (E1, E ′.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Suppose (E1, E ′

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.113055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a8bf016a-0439-420b-9cb0-aedc923904d2 · outbound

This paper cites Ci and Cm, and (E2, E ′.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Ci and Cm, and (E2, E ′

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.104860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1ab896ba-341e-43fd-852b-957a7976d76e · outbound

This paper cites Cm and Co, then (E2 ◦ E1, E ′ 2 ◦ E ′.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Cm and Co, then (E2 ◦ E1, E ′ 2 ◦ E ′

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.097882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 15136db1-bf19-4974-be73-270d9fda4227 · outbound

This paper cites F or any super-operatorE, its dual E † is another super-operator.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality F or any super-operatorE, its dual E † is another super-operator

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.091363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 90105f23-a7f3-43ee-8a6c-2b82a1f3a13e · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 87

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.163180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ee7bd865-b076-48da-957a-bc3271cb3517 · outbound

This paper cites only if” part holds directly by the monotonicity of stab le QOT under data processing [11]. For the “if.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality only if” part holds directly by the monotonicity of stab le QOT under data processing [11]. For the “if

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.083593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation da63ee3e-91e1-4176-a1c0-aea67df7cb97 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 89

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.077189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3b1e09a0-401d-4d9b-8d92-d943ef5e4bd2 · outbound

This paper cites A Q UANTUM RELATIONAL HOARE LOGIC.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A Q UANTUM RELATIONAL HOARE LOGIC

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.070605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c7881317-b8db-4246-bb59-4206fae1b75e · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.064079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 720a155b-1880-4656-bc72-00fb9f55cb85 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 92

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.057071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9f820ce7-6ae7-48af-82a4-c8d4ce22c615 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 93

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.049606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5528dc9e-a130-431e-9442-1586c94cc2d0 · outbound

This paper cites A PPLICATIONS.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality A PPLICATIONS

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.042757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4a965f20-c7fe-4d45-a62d-5f79552ed367 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 95

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.036442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation da9daf10-ff1a-4509-8422-9e7660a602a5 · outbound

This paper cites 3We could also just ask all programs to be interpreted over H = Hall variables, or over H = Hvar(S1)∪ var(S2).

Complete Quantum Relational Hoare Logics from Optimal Transport Duality 3We could also just ask all programs to be interpreted over H = Hall variables, or over H = Hvar(S1)∪ var(S2)

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.029979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation faa33da3-5374-492f-afdb-02e3e68ea4fc · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 97

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.023279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3b747fb8-4eba-4dc2-ac52-5b7230d74e9f · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 98

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.016206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fa2fa603-3f4b-4009-9832-0b4006e390be · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 99

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:24.009501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c62a5a7b-c777-4a4e-9c14-fc3e4d80a3f5 · outbound

This paper cites HerePi,sym =Psym[H[n]−i] ⊗ (Ii⟨1⟩ ⊗Ii⟨2⟩) for i ∈ [n].

Complete Quantum Relational Hoare Logics from Optimal Transport Duality HerePi,sym =Psym[H[n]−i] ⊗ (Ii⟨1⟩ ⊗Ii⟨2⟩) for i ∈ [n]

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:24.002476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3712ac1b-c4ad-4491-a7a1-cf8d2fbd2513 · outbound

This paper cites an unresolved cited work.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Unresolved cited work

Reference 101

Resolution: unresolved; raw_fallback, observed 2026-08-10T14:36:23.994391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation be53c1d9-54a0-43af-9dac-84cf5d17b80c · outbound

This paper cites ﬁnite” component of A, and XA = ∑ λi=+∞Xi is the “inﬁnite.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality ﬁnite” component of A, and XA = ∑ λi=+∞Xi is the “inﬁnite

Reference 102

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:36:23.986205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 58cf7574-a620-4cf8-838b-b4de7fcb00fa · outbound

This paper cites Available: http://dx.doi.org/10.4204/E PTCS.287.2.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Available: http://dx.doi.org/10.4204/E PTCS.287.2

Reference 2019

Resolution: malformed identifier; doi_truncated, observed 2026-08-10T14:36:23.596552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 353268e6-f875-47c2-9bd6-853a7fe2fd2a · outbound

This paper cites Available: https://hal.science/hal-019 63667.

Complete Quantum Relational Hoare Logics from Optimal Transport Duality Available: https://hal.science/hal-019 63667

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-10T14:36:23.379699Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Coverage vector

Reference resolution

Outbound references

Pith citing papers