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Paper Citation Record · LEDGER

Optimal Distributed Similarity Estimation of Quantum Channels

As of 9 August 2026, this Paper Citation Record lists 100 of 107 outbound references and 1 inbound Pith citation observation for arXiv:2512.10465.

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

pith.paper-citation-record.v1
2512.10465 v4

Coverage vector

measured 100 of 107 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T17:21:15.989628Z

measured 101 of 101 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T02:45:06.689198Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T02:48:33.772553Z

Reference resolution

100 of 107 outbound references displayed

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Outbound references

Observation e3f970c4-037b-4dc0-b821-933412344aee · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 1

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source=pdf_text observed=2026-08-03T17:21:06.863153Z digest=sha256:c51b7de240e77a969b672af1e5ae5b6ed53dfbd2df6ca69bf66188c1c247e858

Observation 63fe0f25-a937-4f35-9f81-dbc3367ced2f · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 2

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Observation 55990abc-941c-454d-bd12-13e7d15b586a · outbound

This paper cites Record the measurement results on two devices as |𝜙𝐴⟩ and |𝜙𝐵⟩, and compute ˜𝑓 = |⟨𝜙𝐴|𝜙𝐵⟩| 2.

Optimal Distributed Similarity Estimation of Quantum Channels Record the measurement results on two devices as |𝜙𝐴⟩ and |𝜙𝐵⟩, and compute ˜𝑓 = |⟨𝜙𝐴|𝜙𝐵⟩| 2

Reference 3

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Observation b826d1f7-5a15-48d6-afc1-6ecc639782be · outbound

This paper cites (5) This algorithm requires shared randomness only for state preparation and is described in pseudocode in Algorithm 1.

Optimal Distributed Similarity Estimation of Quantum Channels (5) This algorithm requires shared randomness only for state preparation and is described in pseudocode in Algorithm 1

Reference 4

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Observation 0c6602bf-80f8-4c1f-a653-ec571eb35edc · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 5

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Observation 1c88326a-9ae0-4c8b-97b5-d6cdb1266c49 · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 6

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Observation dd2a80a2-a63f-4630-88bc-5f01504bbf2f · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 7

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Observation cae998ed-71fa-4c96-af74-b52c0f1e8027 · outbound

This paper cites Compute ˜𝑔 = 1 𝑚2 𝑚Õ 𝑖,𝑗 =1 𝟙(𝑎𝑖,𝑏 𝑗), (7) where 𝟙(𝑎,𝑏 ) = 1 if𝑎 =𝑏; otherwise 0.

Optimal Distributed Similarity Estimation of Quantum Channels Compute ˜𝑔 = 1 𝑚2 𝑚Õ 𝑖,𝑗 =1 𝟙(𝑎𝑖,𝑏 𝑗), (7) where 𝟙(𝑎,𝑏 ) = 1 if𝑎 =𝑏; otherwise 0

Reference 8

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Observation 3a088272-008d-4191-ae3e-ae871abe4008 · outbound

This paper cites (8) This incoherent algorithm is summarized in Algorithm 2.

Optimal Distributed Similarity Estimation of Quantum Channels (8) This incoherent algorithm is summarized in Algorithm 2

Reference 9

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Observation ecce942e-afba-4d68-8a47-80c9c47bbf0a · outbound

This paper cites Popkin, Quest for qubits, Science 354, 1090 (2016).

Optimal Distributed Similarity Estimation of Quantum Channels Popkin, Quest for qubits, Science 354, 1090 (2016)

Reference 10

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Observation f2dafab7-1d94-4352-9fc1-b344c5af6f84 · outbound

This paper cites Preskill, Quantum Computing in the NISQ Era and Beyond, Quantum 2, 79 (2018).

Optimal Distributed Similarity Estimation of Quantum Channels Preskill, Quantum Computing in the NISQ Era and Beyond, Quantum 2, 79 (2018)

Reference 11

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Observation d275b449-444f-469b-a6f2-9a0c05cb0f53 · outbound

This paper cites 5 Year Update to the Next Steps in Quantum Computing.

Optimal Distributed Similarity Estimation of Quantum Channels 5 Year Update to the Next Steps in Quantum Computing

Reference 12

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Observation 0e0bb9ce-3362-4db1-bdb0-43b65cf37ee3 · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 13

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Observation 75ef99a8-d9ba-4be7-979d-834f2a2d7dd7 · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 14

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Observation 44c46668-4cb2-44b5-9d35-078ef0f82ce5 · outbound

This paper cites Emerson, M.

Optimal Distributed Similarity Estimation of Quantum Channels Emerson, M

Reference 15

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Observation c945a4e7-d72e-4cb6-ae8d-de6ffd140c6b · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 16

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Observation 89862b75-e89e-4685-ac83-d5c12c8c51e6 · outbound

This paper cites Helsen, I.

Optimal Distributed Similarity Estimation of Quantum Channels Helsen, I

Reference 17

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Observation 2fe60632-e8a8-4d68-b75e-02c7212f8a78 · outbound

This paper cites Pallister, N.

Optimal Distributed Similarity Estimation of Quantum Channels Pallister, N

Reference 18

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Observation 085f0797-1b2f-4eec-8c00-493346ddf6fc · outbound

This paper cites Wang and M.

Optimal Distributed Similarity Estimation of Quantum Channels Wang and M

Reference 19

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Observation 8227d321-d00f-4c08-8aaa-a642a23ad46f · outbound

This paper cites Efficient Verification of Stabilizer Code Subspaces with Local Measurements.

Optimal Distributed Similarity Estimation of Quantum Channels Efficient Verification of Stabilizer Code Subspaces with Local Measurements

Reference 20

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Observation aee9b87b-62c4-4296-8c4b-e84015c28bdd · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 21

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Observation 44dc2dcd-a84a-45ce-866c-f448dff435d1 · outbound

This paper cites Elben, B.

Optimal Distributed Similarity Estimation of Quantum Channels Elben, B

Reference 22

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Observation 0c7d3256-1037-4ca6-84c2-574a8f00cb87 · outbound

This paper cites Knörzer, D.

Optimal Distributed Similarity Estimation of Quantum Channels Knörzer, D

Reference 23

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Observation cf5aabe9-bc26-49a7-b337-1c5eeb2322e4 · outbound

This paper cites Anshu, Z.

Optimal Distributed Similarity Estimation of Quantum Channels Anshu, Z

Reference 24

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 25

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Observation bb2a6a94-371b-43cf-991a-bc38febb5b1d · outbound

This paper cites Zheng, K.

Optimal Distributed Similarity Estimation of Quantum Channels Zheng, K

Reference 26

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Observation 42268549-a561-45e4-af06-00c4fc18a4a5 · outbound

This paper cites Knörzer, X.

Optimal Distributed Similarity Estimation of Quantum Channels Knörzer, X

Reference 27

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Observation 7ec2ea70-129f-449f-8594-1034a3fe0ef4 · outbound

This paper cites Hinsche, M.

Optimal Distributed Similarity Estimation of Quantum Channels Hinsche, M

Reference 28

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Observation 41717681-7ca4-4f22-a64e-eebf2b492c26 · outbound

This paper cites State Similarity in Modular Superconducting Quantum Processors with Classical Communications.

Optimal Distributed Similarity Estimation of Quantum Channels State Similarity in Modular Superconducting Quantum Processors with Classical Communications

Reference 29

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Observation 2edd8cb0-1cfb-49fc-a66f-1258be78507e · outbound

This paper cites On the sample complexity of purity and inner product estimation.

Optimal Distributed Similarity Estimation of Quantum Channels On the sample complexity of purity and inner product estimation

Reference 30

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Observation e008e1b1-5b7f-4c1f-bde0-f7d637778bcc · outbound

This paper cites Distributed inner product estimation with limited quantum communication.

Optimal Distributed Similarity Estimation of Quantum Channels Distributed inner product estimation with limited quantum communication

Reference 31

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Observation bc879dbc-fd6e-4a38-bc04-01e5e9ba32af · outbound

This paper cites Dalton, J.

Optimal Distributed Similarity Estimation of Quantum Channels Dalton, J

Reference 32

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Observation 2ae5385a-3922-4faa-9479-9a0edbbdddf1 · outbound

This paper cites Zheng, X.

Optimal Distributed Similarity Estimation of Quantum Channels Zheng, X

Reference 33

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Observation b2b10ee0-0725-4fa8-8a64-9a9b21a08421 · outbound

This paper cites Angrisani, Learning unitaries with quantum statistical queries, Quantum 9, 1817 (2025).

Optimal Distributed Similarity Estimation of Quantum Channels Angrisani, Learning unitaries with quantum statistical queries, Quantum 9, 1817 (2025)

Reference 34

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Observation e96f0ab8-17c2-4f4a-9cd6-484c9c0cd922 · outbound

This paper cites Sun and Z.

Optimal Distributed Similarity Estimation of Quantum Channels Sun and Z

Reference 35

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Observation 78cd68f2-f70d-4fe1-95c2-cbe0bc893528 · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 36

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 37

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Observation 6eb566b9-cc61-4cf3-8790-1e2651b743d0 · outbound

This paper cites Eisert, D.

Optimal Distributed Similarity Estimation of Quantum Channels Eisert, D

Reference 38

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Observation 4002a43c-932d-4795-953b-58cac00172ea · outbound

This paper cites Fawzi, N.

Optimal Distributed Similarity Estimation of Quantum Channels Fawzi, N

Reference 39

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Observation d5b7ffaa-1953-423e-96d9-e02ca20fc96f · outbound

This paper cites Kliesch and I.

Optimal Distributed Similarity Estimation of Quantum Channels Kliesch and I

Reference 40

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Observation f022d31f-5601-461e-9f00-fdafe7277e70 · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 41

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Observation 9c8b12f8-3b36-46d1-a8f7-744c5500fe0d · outbound

This paper cites Quantum Channel Testing in Average-Case Distance.

Optimal Distributed Similarity Estimation of Quantum Channels Quantum Channel Testing in Average-Case Distance

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Observation 8b5b31dd-80a9-4dc2-a2e5-9cc3adb1d9f3 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 43

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Observation aea8e740-5d8d-4e0b-809c-b634eda89eda · outbound

This paper cites Kunjummen, M.

Optimal Distributed Similarity Estimation of Quantum Channels Kunjummen, M

Reference 44

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Observation 1d7085d6-4f5c-4019-a0e8-e4c922fe7a41 · outbound

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Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 45

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Observation 3ba71848-772d-4a8a-b233-5172891526f3 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 46

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Observation 519e1e03-ffb4-4b30-b3c7-70688107cdc9 · outbound

This paper cites Elben, S.

Optimal Distributed Similarity Estimation of Quantum Channels Elben, S

Reference 47

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Observation c3fd7d19-f169-4595-8762-cf6c8e08ca10 · outbound

This paper cites Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Reports on Mathe- matical Physics 3, 275 (1972).

Optimal Distributed Similarity Estimation of Quantum Channels Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Reports on Mathe- matical Physics 3, 275 (1972)

Reference 48

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Observation a376a31d-45d2-4354-9338-57d6087a5e9a · outbound

This paper cites Liang, Y .-H.

Optimal Distributed Similarity Estimation of Quantum Channels Liang, Y .-H

Reference 49

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Observation b5a224eb-cd51-493c-bc5d-6516a11289b7 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 50

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Observation d8a9f1dc-8a74-4c10-b968-e47f1f52e0de · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 51

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Observation 47f6c79d-a276-4d19-b159-1f0434b679ef · outbound

This paper cites Huang, M.

Optimal Distributed Similarity Estimation of Quantum Channels Huang, M

Reference 52

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Observation c5744843-f99c-4791-946a-3b7007ecb9cc · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 53

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Observation 3334eb6d-ea05-4abf-a0ed-871c923b178c · outbound

This paper cites Jeon and C.

Optimal Distributed Similarity Estimation of Quantum Channels Jeon and C

Reference 54

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Observation 037cc945-7aa8-4c7c-9d15-a5ad8dd8ef73 · outbound

This paper cites Yu, Assouad, fano, and le cam, in Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics(Springer New Y ork, 1997) pp.

Optimal Distributed Similarity Estimation of Quantum Channels Yu, Assouad, fano, and le cam, in Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics(Springer New Y ork, 1997) pp

Reference 55

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Observation 8c32fd70-26e5-4485-ac78-3917ee73cb00 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 56

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Observation 18b2e56c-b1d8-49a5-b64b-cb6c8fa54651 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 57

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Observation 16ca66b2-8c8a-40ae-9699-1c54841bbc48 · outbound

This paper cites Chen and W.

Optimal Distributed Similarity Estimation of Quantum Channels Chen and W

Reference 58

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Observation 5556cd6b-abd8-4162-a9ef-4b53a9f12ded · outbound

This paper cites Schuster, J.

Optimal Distributed Similarity Estimation of Quantum Channels Schuster, J

Reference 59

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Observation 0c0602b8-27b5-4352-a9d6-53481a7c49a3 · outbound

This paper cites The Church of the Symmetric Subspace.

Optimal Distributed Similarity Estimation of Quantum Channels The Church of the Symmetric Subspace

Reference 60

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Observation 299c8205-c2cc-4072-a107-08daec9e3558 · outbound

This paper cites Grier, H.

Optimal Distributed Similarity Estimation of Quantum Channels Grier, H

Reference 61

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Observation 2a157183-ce2b-42d7-bd34-fa3693dbce9e · outbound

This paper cites Conjugate queries can help.

Optimal Distributed Similarity Estimation of Quantum Channels Conjugate queries can help

Reference 62

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Observation d071e2bd-c188-4dfa-a81e-ac3205994f0a · outbound

This paper cites Pelecanos, J.

Optimal Distributed Similarity Estimation of Quantum Channels Pelecanos, J

Reference 63

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Observation ca5d05be-0dfe-47e2-a656-148904c97c2f · outbound

This paper cites Ananth, A.

Optimal Distributed Similarity Estimation of Quantum Channels Ananth, A

Reference 64

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Observation 4e6e61be-d75b-4368-bc17-fda86110181d · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 65

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Observation 42ad6b14-8078-4731-939f-6c04fe52e3df · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 66

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Observation 6e743c00-bdf9-49de-b590-51c3d4c3b971 · outbound

This paper cites Chiribella, On quantum estimation, quantum cloning and fi- nite quantum de finetti theorems, in Theory of Quantum Com- putation, Communication, and Cryptography, edited by W.

Optimal Distributed Similarity Estimation of Quantum Channels Chiribella, On quantum estimation, quantum cloning and fi- nite quantum de finetti theorems, in Theory of Quantum Com- putation, Communication, and Cryptography, edited by W

Reference 67

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Observation a1b5b42b-aa13-4174-a53b-d45b88d13d97 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 68

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Observation 3301f665-e075-4c03-a231-5f5ba9f70532 · outbound

This paper cites Lower Bound 10.

Optimal Distributed Similarity Estimation of Quantum Channels Lower Bound 10

Reference 69

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Observation 68d3afc7-9805-41d0-b139-4a6547d7d970 · outbound

This paper cites Proof of Theorem 1 11 b.

Optimal Distributed Similarity Estimation of Quantum Channels Proof of Theorem 1 11 b

Reference 70

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Observation cee03e8a-d084-48a0-bce6-ea263c47a7a2 · outbound

This paper cites Proof of Theorem 2 13 b.

Optimal Distributed Similarity Estimation of Quantum Channels Proof of Theorem 2 13 b

Reference 71

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Observation 260b161d-acb9-489c-8705-bb83ed23ea68 · outbound

This paper cites Distinguishing Problem for Estimation 17 b.

Optimal Distributed Similarity Estimation of Quantum Channels Distinguishing Problem for Estimation 17 b

Reference 72

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Observation 851371ef-307d-43a2-9d19-61d544d93911 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 73

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Observation f2f0b41c-82be-4810-a553-1fcd8df33d7a · outbound

This paper cites DSEC with Independent Classical Shadow 23.

Optimal Distributed Similarity Estimation of Quantum Channels DSEC with Independent Classical Shadow 23

Reference 74

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Observation 0e8b24e5-234a-43ff-85da-47ee55e5f595 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 75

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source=pdf_text observed=2026-08-03T17:21:13.249412Z digest=sha256:e7e605c7b13bbfb2030d1344a3df88339f621dae9e7ffa7df2819f51153c0035

Observation 28dbaa7d-8ba3-41ff-80d0-dd6e10821b48 · outbound

This paper cites Then, we introduce two central tools utilized in this work: the Haar measure and approximate unitary designs.

Optimal Distributed Similarity Estimation of Quantum Channels Then, we introduce two central tools utilized in this work: the Haar measure and approximate unitary designs

Reference 76

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source=pdf_text observed=2026-08-03T17:21:13.404310Z digest=sha256:ecafc4b29eac3b225268c2d998ccb0c163cdfb25020456cadf86ddf74c67f00a

Observation 3118fdbf-b880-4365-8594-8e86371ea122 · outbound

This paper cites The set of Hermitian operators on H is denoted by B (H ), and the set of density matrices on H is denoted by D (H ).

Optimal Distributed Similarity Estimation of Quantum Channels The set of Hermitian operators on H is denoted by B (H ), and the set of density matrices on H is denoted by D (H )

Reference 77

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Observation 40ef6ad9-7546-4e1d-ac86-c5eb500edc51 · outbound

This paper cites The Haar random channel is defined as E (𝑘) 𝐻 (𝐴) := 𝔼𝑈∼𝜇𝐻𝑈 ⊗𝑘𝐴𝑈†⊗𝑘, 𝐴 ∈ B (H ⊗𝑘).

Optimal Distributed Similarity Estimation of Quantum Channels The Haar random channel is defined as E (𝑘) 𝐻 (𝐴) := 𝔼𝑈∼𝜇𝐻𝑈 ⊗𝑘𝐴𝑈†⊗𝑘, 𝐴 ∈ B (H ⊗𝑘)

Reference 78

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source=pdf_text observed=2026-08-03T17:21:13.722163Z digest=sha256:21a34f5601af2e2a8b3822d65b26fa32c2626d81e0987d00c7c04d3d12c81f98

Observation b82d0637-8c12-48fb-9c95-e27275a8e824 · outbound

This paper cites Here E1 ⪯ E 2 denotes that E2 − E 1 is a completely-positive map.

Optimal Distributed Similarity Estimation of Quantum Channels Here E1 ⪯ E 2 denotes that E2 − E 1 is a completely-positive map

Reference 79

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source=pdf_text observed=2026-08-03T17:21:13.896402Z digest=sha256:4c36ad8527cc8a581cefcb767608d95dd4c7a5a6be200fa3e8ec1551a420a5c4

Observation 76ad78b7-80e3-48b2-b3b6-7d3cde84f417 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 80

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source=pdf_text observed=2026-08-03T17:21:14.019895Z digest=sha256:2a47bb095878fc18139d5d878122ad6fa065f77c863fb2db2e01fb4b389bfc52

Observation 10e87d58-afc5-4566-9a27-0cc7c4dfbd5f · outbound

This paper cites Define the Choi operators of𝑈 and𝑉 as𝐽𝑈 and𝐽𝑉 , respectively.

Optimal Distributed Similarity Estimation of Quantum Channels Define the Choi operators of𝑈 and𝑉 as𝐽𝑈 and𝐽𝑉 , respectively

Reference 81

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Observation 5f1d5967-f8fb-4bca-88ab-840f7fcb80d8 · outbound

This paper cites First, we introduce the tree representation of channel learning with incoherent access, which is a powerful tool in proving lower bounds for learning tasks [ 41, 44, 47–49].

Optimal Distributed Similarity Estimation of Quantum Channels First, we introduce the tree representation of channel learning with incoherent access, which is a powerful tool in proving lower bounds for learning tasks [ 41, 44, 47–49]

Reference 82

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source=pdf_text observed=2026-08-03T17:21:14.326040Z digest=sha256:d55867925a8f36c1bf299bd5d9d5f299f62f38e1751c2d7e54c57406dd6cf850

Observation 48a211db-5e06-43e5-bc08-9c2e34823005 · outbound

This paper cites 𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 − 𝑝D TV = 1 2 Õ ℓ 𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 (ℓ) − 𝑝D (ℓ) (B16) = Õ ℓ:𝑝D (ℓ) ≥𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 (ℓ) 𝑝D (ℓ) 1 − 𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 (ℓ) 𝑝D (ℓ).

Optimal Distributed Similarity Estimation of Quantum Channels 𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 − 𝑝D TV = 1 2 Õ ℓ 𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 (ℓ) − 𝑝D (ℓ) (B16) = Õ ℓ:𝑝D (ℓ) ≥𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 (ℓ) 𝑝D (ℓ) 1 − 𝔼𝑈∼𝜇𝐻𝑝𝑈,𝑈 (ℓ) 𝑝D (ℓ)

Reference 83

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source=pdf_text observed=2026-08-03T17:21:14.434610Z digest=sha256:e13f0b0b6b742da2a4743e93802b5285ce4fe875b192290e50412c30ea828efc

Observation cec808c4-e7c1-41ef-9c21-7da5f96fa18f · outbound

This paper cites (B26) Therefore, we have 𝑝D − 𝔼𝑈,𝑉 ∼𝜇𝐻𝑝𝑈,𝑉 TV ≤ 1 − 1 − 𝑇 2 𝑑 2 ≤ 2𝑇 2 𝑑.

Optimal Distributed Similarity Estimation of Quantum Channels (B26) Therefore, we have 𝑝D − 𝔼𝑈,𝑉 ∼𝜇𝐻𝑝𝑈,𝑉 TV ≤ 1 − 1 − 𝑇 2 𝑑 2 ≤ 2𝑇 2 𝑑

Reference 84

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source=pdf_text observed=2026-08-03T17:21:14.571401Z digest=sha256:64cd21e02d0e45523299b283d42e01bd16c7346cdc2334336b55ec9b141130db

Observation e19be8b4-d423-45f3-bf1e-b4e28564397f · outbound

This paper cites measure-and-prepare.

Optimal Distributed Similarity Estimation of Quantum Channels measure-and-prepare

Reference 85

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source=pdf_text observed=2026-08-03T17:21:14.667368Z digest=sha256:6185643debeed00e465fdcbb76a85d149b35eb8b3948afd0f5ec2498d4562ab8

Observation 76686af4-cd1d-4e43-ad0b-deb48e388c28 · outbound

This paper cites The proof is similar to [ 15].

Optimal Distributed Similarity Estimation of Quantum Channels The proof is similar to [ 15]

Reference 86

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source=pdf_text observed=2026-08-03T17:21:14.817256Z digest=sha256:eccd92814a7326cdcb316d101f9e6e8e8f7027d7c9349e69366c740e03970222

Observation 8eb60998-6818-41ab-877d-d9ce58aa958b · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 87

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source=pdf_text observed=2026-08-03T17:21:14.937908Z digest=sha256:5ae7269b70aaf8475d01e1d2caf2aba7097057c2a05995a019fb94f18739fcc6

Observation f5e3819c-804d-4c11-a782-ddc9649c2a2a · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 88

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source=pdf_text observed=2026-08-03T17:21:15.058194Z digest=sha256:2729cd41676de451d9d93d0195cfa965df8015f2a5a94bf00fe40e8005590fb7

Observation c72e3aa4-d384-4d4e-b197-08190daf3e71 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 89

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source=pdf_text observed=2026-08-03T17:21:15.151171Z digest=sha256:bd2500e195c515268bae66ba05a0313832df1858dd028cacad544bdb837fcf8e

Observation 27aea66f-5080-4538-b9fc-085b2a6d4299 · outbound

This paper cites The performance of the estimation algorithm 𝔸 guarantees that if the result 𝑓 is in case 𝑖(𝑖 = 1, 2), then |𝑓 − 𝑓𝑖| ≤ 𝜀/100 holds with probability at least 0.99.

Optimal Distributed Similarity Estimation of Quantum Channels The performance of the estimation algorithm 𝔸 guarantees that if the result 𝑓 is in case 𝑖(𝑖 = 1, 2), then |𝑓 − 𝑓𝑖| ≤ 𝜀/100 holds with probability at least 0.99

Reference 90

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source=pdf_text observed=2026-08-03T17:21:15.226853Z digest=sha256:702c4cab3c4050085a63e66dd1c12b92391187ca09f9417ee116e0f973f59c67

Observation a3e0b05b-30e2-46c7-9c80-d38f353f3b57 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 91

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source=pdf_text observed=2026-08-03T17:21:15.305013Z digest=sha256:c303377359f2efb78777288df5ad8ad5d0e7ea6c09be1872d410baccd9bc9527

Observation 0985e9f0-8f2f-4155-bfcf-5eb0bb4e8032 · outbound

This paper cites It should be noted that Problem 2 is equivalent to Problem 3, as these two problems have the same average inputs.

Optimal Distributed Similarity Estimation of Quantum Channels It should be noted that Problem 2 is equivalent to Problem 3, as these two problems have the same average inputs

Reference 92

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source=pdf_text observed=2026-08-03T17:21:15.394773Z digest=sha256:879729c15e2b40d7d98c30665887e57a2f129f743191723438df4a224aa7056e

Observation e3988491-9e42-4ef8-810a-44dcc0011dc0 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 93

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source=pdf_text observed=2026-08-03T17:21:15.473691Z digest=sha256:9cdb41f7246dac028f52f300d3681cdb48faaa5499572f1bc7cf7006fa2c68c9

Observation c334e820-664a-4fb2-a77e-241c32479fcc · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 94

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Observation a804b264-aaf4-49f0-b785-968e54b6e4dc · outbound

This paper cites It should be noted that we can simulate the input of Problem 3 with high probability, since 𝐾 = 100𝑇𝜀 + 100 ⇒𝑡 ≤ 𝐾 with high probability.

Optimal Distributed Similarity Estimation of Quantum Channels It should be noted that we can simulate the input of Problem 3 with high probability, since 𝐾 = 100𝑇𝜀 + 100 ⇒𝑡 ≤ 𝐾 with high probability

Reference 95

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source=pdf_text observed=2026-08-03T17:21:15.632169Z digest=sha256:2d31fcc770a37fe0c6897a6cda2727e949e1978cd473d684f5eeecdafe4bfd8d

Observation b3decc81-e846-423d-8b52-b1bb0bbe4e53 · outbound

This paper cites Let 𝐽𝑈 and 𝐽𝑉 be the Choi operators of channels U and V.

Optimal Distributed Similarity Estimation of Quantum Channels Let 𝐽𝑈 and 𝐽𝑉 be the Choi operators of channels U and V

Reference 96

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Observation cc5eba8a-ecdf-4b8a-ada6-f1ac4e25f115 · outbound

This paper cites The algorithm solving DSEC with incoherent access is summarized in Algorithm 2.

Optimal Distributed Similarity Estimation of Quantum Channels The algorithm solving DSEC with incoherent access is summarized in Algorithm 2

Reference 97

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Observation 67954322-5895-41f3-b6f5-ebd37ee4575a · outbound

This paper cites (C31) As shown in Eq.

Optimal Distributed Similarity Estimation of Quantum Channels (C31) As shown in Eq

Reference 98

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source=pdf_text observed=2026-08-03T17:21:15.819814Z digest=sha256:a3f032d6b0c085d42d86dcac040c171ec34c9ace82b7717d3b57308f3cd4f7f9

Observation a15f14f9-9b5e-4d2d-9394-39d7c56af5c3 · outbound

This paper cites an unresolved cited work.

Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work

Reference 99

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source=pdf_text observed=2026-08-03T17:21:15.903687Z digest=sha256:69ced3fee75c19c56971c05f47066edabbc5ce9074144b2dbde69fbe3e4e1262

Observation 7b2f071b-0394-44ae-b64e-9b229ee34f52 · outbound

This paper cites Given an unknown unitary channel U (·) = 𝑈 (·)𝑈†, we can obtain the following classical snapshot by inputting the state |𝜓⟩⊗𝑠 and performing the POVM M𝑠 (defined in Eq.

Optimal Distributed Similarity Estimation of Quantum Channels Given an unknown unitary channel U (·) = 𝑈 (·)𝑈†, we can obtain the following classical snapshot by inputting the state |𝜓⟩⊗𝑠 and performing the POVM M𝑠 (defined in Eq

Reference 100

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source=pdf_text observed=2026-08-03T17:21:15.989628Z digest=sha256:7fc64d5ed64a667fa101383330f8ef58277784b39a73670f6d250c6c7bedd4c7

Pith citing papers

Observation c0847e57-38ff-4965-a79c-5571c7bf42c0 · inbound

Worst-Case Sample Complexity Bounds for Distributed Inner Product Estimation with Local Randomized Measurements cites this paper.

Worst-Case Sample Complexity Bounds for Distributed Inner Product Estimation with Local Randomized Measurements Optimal Distributed Similarity Estimation of Quantum Channels

Reference 13

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arxiv_id, observed 2026-06-03T02:05:11.936047Z

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source=pdf_text observed=2026-05-15T02:45:06.689198Z digest=sha256:420ee657abf5d3e26f4dc4f98b8d0dadc0873689663f986a3df826960ed1c33b