Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T17:21:15.989628Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T17:21:15.989628Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-15T02:45:06.689198Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-15T02:48:33.772553Z
100 of 107 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e3f970c4-037b-4dc0-b821-933412344aee · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 1
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Observation 63fe0f25-a937-4f35-9f81-dbc3367ced2f · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 2
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Observation 55990abc-941c-454d-bd12-13e7d15b586a · outbound
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
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 5
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Observation 1c88326a-9ae0-4c8b-97b5-d6cdb1266c49 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 6
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Observation dd2a80a2-a63f-4630-88bc-5f01504bbf2f · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 7
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Observation cae998ed-71fa-4c96-af74-b52c0f1e8027 · outbound
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
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
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
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
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 13
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Observation 75ef99a8-d9ba-4be7-979d-834f2a2d7dd7 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 14
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Observation 44c46668-4cb2-44b5-9d35-078ef0f82ce5 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Emerson, M
Reference 15
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Observation c945a4e7-d72e-4cb6-ae8d-de6ffd140c6b · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 16
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Observation 89862b75-e89e-4685-ac83-d5c12c8c51e6 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Helsen, I
Reference 17
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Observation 2fe60632-e8a8-4d68-b75e-02c7212f8a78 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Pallister, N
Reference 18
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Observation 085f0797-1b2f-4eec-8c00-493346ddf6fc · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Wang and M
Reference 19
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Observation 8227d321-d00f-4c08-8aaa-a642a23ad46f · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 21
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Observation 44dc2dcd-a84a-45ce-866c-f448dff435d1 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Elben, B
Reference 22
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Observation 0c7d3256-1037-4ca6-84c2-574a8f00cb87 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Knörzer, D
Reference 23
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Observation cf5aabe9-bc26-49a7-b337-1c5eeb2322e4 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Anshu, Z
Reference 24
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Observation 8b0ff2ea-541b-46cc-8801-3165c7d660ac · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 25
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Observation bb2a6a94-371b-43cf-991a-bc38febb5b1d · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Zheng, K
Reference 26
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Observation 42268549-a561-45e4-af06-00c4fc18a4a5 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Knörzer, X
Reference 27
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Observation 7ec2ea70-129f-449f-8594-1034a3fe0ef4 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Hinsche, M
Reference 28
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Observation 41717681-7ca4-4f22-a64e-eebf2b492c26 · outbound
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
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
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
Optimal Distributed Similarity Estimation of Quantum Channels Dalton, J
Reference 32
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Observation 2ae5385a-3922-4faa-9479-9a0edbbdddf1 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Zheng, X
Reference 33
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Observation b2b10ee0-0725-4fa8-8a64-9a9b21a08421 · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Sun and Z
Reference 35
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Observation 78cd68f2-f70d-4fe1-95c2-cbe0bc893528 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 36
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Observation 0881ac84-2c17-4cdb-b6cd-5908b1b498aa · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 37
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Observation 6eb566b9-cc61-4cf3-8790-1e2651b743d0 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Eisert, D
Reference 38
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Observation 4002a43c-932d-4795-953b-58cac00172ea · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Fawzi, N
Reference 39
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Observation d5b7ffaa-1953-423e-96d9-e02ca20fc96f · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Kliesch and I
Reference 40
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Observation f022d31f-5601-461e-9f00-fdafe7277e70 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 41
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Observation 9c8b12f8-3b36-46d1-a8f7-744c5500fe0d · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Quantum Channel Testing in Average-Case Distance
Reference 42
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Observation 8b5b31dd-80a9-4dc2-a2e5-9cc3adb1d9f3 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 43
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Observation aea8e740-5d8d-4e0b-809c-b634eda89eda · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Kunjummen, M
Reference 44
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Observation 1d7085d6-4f5c-4019-a0e8-e4c922fe7a41 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 45
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Observation 3ba71848-772d-4a8a-b233-5172891526f3 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 46
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Observation 519e1e03-ffb4-4b30-b3c7-70688107cdc9 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Elben, S
Reference 47
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Observation c3fd7d19-f169-4595-8762-cf6c8e08ca10 · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Liang, Y .-H
Reference 49
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Observation b5a224eb-cd51-493c-bc5d-6516a11289b7 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 50
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Observation d8a9f1dc-8a74-4c10-b968-e47f1f52e0de · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 51
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Observation 47f6c79d-a276-4d19-b159-1f0434b679ef · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Huang, M
Reference 52
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Observation c5744843-f99c-4791-946a-3b7007ecb9cc · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 53
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Observation 3334eb6d-ea05-4abf-a0ed-871c923b178c · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Jeon and C
Reference 54
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Observation 037cc945-7aa8-4c7c-9d15-a5ad8dd8ef73 · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 56
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Observation 18b2e56c-b1d8-49a5-b64b-cb6c8fa54651 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 57
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Observation 16ca66b2-8c8a-40ae-9699-1c54841bbc48 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Chen and W
Reference 58
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Observation 5556cd6b-abd8-4162-a9ef-4b53a9f12ded · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Schuster, J
Reference 59
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Observation 0c0602b8-27b5-4352-a9d6-53481a7c49a3 · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Grier, H
Reference 61
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Observation 2a157183-ce2b-42d7-bd34-fa3693dbce9e · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Conjugate queries can help
Reference 62
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Observation d071e2bd-c188-4dfa-a81e-ac3205994f0a · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Pelecanos, J
Reference 63
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Observation ca5d05be-0dfe-47e2-a656-148904c97c2f · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Ananth, A
Reference 64
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Observation 4e6e61be-d75b-4368-bc17-fda86110181d · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 65
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Observation 42ad6b14-8078-4731-939f-6c04fe52e3df · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 66
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Observation 6e743c00-bdf9-49de-b590-51c3d4c3b971 · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 68
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Observation 3301f665-e075-4c03-a231-5f5ba9f70532 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Lower Bound 10
Reference 69
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Observation 68d3afc7-9805-41d0-b139-4a6547d7d970 · outbound
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
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
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 73
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Observation f2f0b41c-82be-4810-a553-1fcd8df33d7a · outbound
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
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 75
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Observation 28dbaa7d-8ba3-41ff-80d0-dd6e10821b48 · outbound
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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Observation 3118fdbf-b880-4365-8594-8e86371ea122 · outbound
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
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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Observation b82d0637-8c12-48fb-9c95-e27275a8e824 · outbound
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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Observation 76ad78b7-80e3-48b2-b3b6-7d3cde84f417 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 80
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Observation 10e87d58-afc5-4566-9a27-0cc7c4dfbd5f · outbound
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
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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Observation 48a211db-5e06-43e5-bc08-9c2e34823005 · outbound
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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Observation cec808c4-e7c1-41ef-9c21-7da5f96fa18f · outbound
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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Observation e19be8b4-d423-45f3-bf1e-b4e28564397f · outbound
Optimal Distributed Similarity Estimation of Quantum Channels measure-and-prepare
Reference 85
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Observation 76686af4-cd1d-4e43-ad0b-deb48e388c28 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels The proof is similar to [ 15]
Reference 86
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Observation 8eb60998-6818-41ab-877d-d9ce58aa958b · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 87
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Observation f5e3819c-804d-4c11-a782-ddc9649c2a2a · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 88
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Observation c72e3aa4-d384-4d4e-b197-08190daf3e71 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 89
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Observation 27aea66f-5080-4538-b9fc-085b2a6d4299 · outbound
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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Observation a3e0b05b-30e2-46c7-9c80-d38f353f3b57 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 91
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Observation 0985e9f0-8f2f-4155-bfcf-5eb0bb4e8032 · outbound
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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Observation e3988491-9e42-4ef8-810a-44dcc0011dc0 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 93
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Observation c334e820-664a-4fb2-a77e-241c32479fcc · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 94
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Observation a804b264-aaf4-49f0-b785-968e54b6e4dc · outbound
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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Observation b3decc81-e846-423d-8b52-b1bb0bbe4e53 · outbound
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
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
Optimal Distributed Similarity Estimation of Quantum Channels (C31) As shown in Eq
Reference 98
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Observation a15f14f9-9b5e-4d2d-9394-39d7c56af5c3 · outbound
Optimal Distributed Similarity Estimation of Quantum Channels Unresolved cited work
Reference 99
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Observation 7b2f071b-0394-44ae-b64e-9b229ee34f52 · outbound
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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Observation c0847e57-38ff-4965-a79c-5571c7bf42c0 · inbound
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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