Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:02:14.954263Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 77 of 77 outbound references and 1 inbound Pith citation observation for arXiv:2507.19454.
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 2026-08-15T18:02:14.954263Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T04:05:36.298226Z
A source-named dated measurement, never combined with another source.
Source: cited_works
77 of 77 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 54b59bb3-8c6e-45d2-93f9-06d727da9b3d · outbound
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8b1028dc-5396-420f-a2bb-eb5014c2e51d · outbound
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4b0cfe51-b167-4f67-92a1-19145c2a04ba · outbound
Random approximate quantum information masking Unresolved cited work
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 99e00b92-6956-4c9a-8cba-8e1be16c910b · outbound
Random approximate quantum information masking DiVincenzo, D
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bdeb1fb8-894b-471e-bc6f-0b3b661fd163 · outbound
Random approximate quantum information masking Lloyd, Capacity of the noisy quantum channel, Phys
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ee79909b-39ea-4f98-83ef-61dab810a27b · outbound
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dd3ae109-1e08-4bcc-a135-f90b78fa46b7 · outbound
Random approximate quantum information masking Quantum coding theorem from privacy and distinguishability
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 73765b60-9422-4246-8ce6-7997ccb61530 · outbound
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b6a18121-b341-4fbe-83e6-1ffd90efdb90 · outbound
Random approximate quantum information masking Both terms cannot be made small simultaneously irrespective of the choices of d1, d2, and dC, as illustrated in Fig
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1aa31365-e3d7-4c5a-9f6d-389d8209b5df · outbound
Random approximate quantum information masking Hayden and J
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bd18e80b-fa02-4970-bfd7-c256adc45764 · outbound
Random approximate quantum information masking Sekino and L
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2b7011ce-0fc0-4bd1-9a52-748c88586126 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ae6c8a50-21ee-45a1-aab6-563a4546e0df · outbound
Random approximate quantum information masking Stabilizer Codes and Quantum Error Correction
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 722836cf-bd37-4cb6-936a-9e70e306c25a · outbound
Random approximate quantum information masking Knill and R
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e484d0a-02a4-4d84-b3cf-79005b4f5372 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 346c04f8-16e4-42ae-8988-65e4614c1963 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7cd0165c-f8e7-47bd-8275-7f5b3377d86f · outbound
Random approximate quantum information masking Unresolved cited work
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5daee4f5-d0cb-4ad1-8bfb-62cf8ad98094 · outbound
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4afe23f4-419e-414a-9e17-539b3137a93a · outbound
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 873aa560-3ddb-4ba0-8dde-b26d891cf132 · outbound
Random approximate quantum information masking Zhu, Hiding and masking quantum information in complex and real quantum mechanics, Phys
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2b269db6-db8a-4e4c-a0d2-04d2b86dc582 · outbound
Random approximate quantum information masking Li and Y.-L
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a7393def-d895-4ccf-b361-226307fa34d2 · outbound
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7009c7cc-1a22-4875-9fac-ce220c34a356 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 69b49a50-81cb-45d9-aa97-0409d6b8a43d · outbound
Random approximate quantum information masking Srednicki, Chaos and quantum thermalization, Phys
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a754f0e3-f78e-4a80-b56a-b7b1038980cc · outbound
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 93488fcd-e918-4b52-9f41-1bfadabd8198 · outbound
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f514d27d-7502-448d-ba9f-d29d9e684d81 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 770120ad-44b8-4272-beca-29512176ebf6 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dbbdfa76-2a9c-4071-91cc-cbf50e801862 · outbound
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 134f1e56-cd8d-4373-89f6-f59126eec730 · outbound
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dc81f733-66a8-4054-8124-703607f9095b · outbound
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7a022d69-6ce5-4504-89e8-411186cdfab6 · outbound
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8ec0af9a-a081-4511-86f4-562d84d96182 · outbound
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 53536ded-a6a8-4333-bc6d-f5bc1b340678 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 01ec6add-2c37-438c-9ad3-3cbd5a3acec0 · outbound
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a8bb70a7-3e51-4c39-b886-424aac9fa142 · outbound
Random approximate quantum information masking Kong and Z.-W
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 378224a7-5474-459d-9d59-2af50ec63a3b · outbound
Random approximate quantum information masking Brown and O
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 25836a9c-0533-4617-94b2-9275a702e56e · outbound
Random approximate quantum information masking Brown and O
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 56218f31-cc16-4d92-8861-1c61ff254250 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2cea8904-c2e6-4929-ac81-9805e3c4c30f · outbound
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 839e28e7-7294-41d5-b4c2-6d7ed0d5ec67 · outbound
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 762e2d7d-ed08-4352-b516-08b537002194 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 513b1191-d03d-4991-b321-96e23585843b · outbound
Random approximate quantum information masking Schumacher and M
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f20e9c24-3635-4226-9527-6eb3fbf5f3df · outbound
Random approximate quantum information masking Cr´ epeau, D
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7a6f7dca-5c45-40c6-b75b-fd7f7e2287e9 · outbound
Random approximate quantum information masking Klesse, Approximate quantum error correction, ran- dom codes, and quantum channel capacity, Phys
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b2f89fbd-cf39-4bd2-ab75-cb1d3a95f6f2 · outbound
Random approximate quantum information masking B´ eny and O
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 376b098b-1eef-4606-858e-f2b12a17a5d6 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 61e382ca-6f06-4144-b543-e4fa7dac0465 · outbound
Random approximate quantum information masking B´ eny and O
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7c718edd-3d28-41cf-b306-23bc67710100 · outbound
Random approximate quantum information masking B´ eny, Perturbative quantum error correction, Phys
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 413f8436-3780-4c42-bf28-26778fdaa3b8 · outbound
Random approximate quantum information masking Mandayam and H
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cb05a9ca-8fcc-42e5-af03-adb9feb64414 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 71059638-b992-4fd1-ae38-6f7d2eafec2e · outbound
Random approximate quantum information masking Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 53fb6ed3-a82b-4d3e-911f-6480611bc26a · outbound
Random approximate quantum information masking Unresolved cited work
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9c4e0862-0e0d-4fad-a417-4bd6afc426ba · outbound
Random approximate quantum information masking Unresolved cited work
Reference 54
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bdf47066-c4d5-45b5-8445-b57e9a95a14d · outbound
Random approximate quantum information masking Unresolved cited work
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f989cae2-fccc-4e74-9d0d-dc41f2f133df · outbound
Random approximate quantum information masking Unresolved cited work
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2ac41885-5d9e-415f-b850-1bac00ef7a37 · outbound
Random approximate quantum information masking Zhu and B.-G
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1081e2e3-316e-48f2-892c-043fda0b4b12 · outbound
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b223caf6-b63b-4820-b78e-5e4b5d441f7e · outbound
Random approximate quantum information masking Absolutely Maximally Entangled States: Existence and Applications
Reference 59
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39c1a507-c8e9-482f-aa45-986345169f50 · outbound
Random approximate quantum information masking Aubrun and S
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5adaeb72-c695-400a-bf54-95dc84ed58e3 · outbound
Random approximate quantum information masking Tomamichel, R
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8d066522-56fa-478a-8502-1f9e9fee9c25 · outbound
Random approximate quantum information masking Wang, Universal quantum computing models: a perspective of resource theory, Acta Phys
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ecf1f34e-1768-4c82-af3d-1fccbcade730 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 753a05c4-afd2-4561-a296-2db621bd5df4 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation dfa450f0-902c-4f6b-a424-bd53722f20bc · outbound
Random approximate quantum information masking Proof of Proposition 2 First, we introduce the following lemma, which allows us to deal with the expectation value taken over the random subspace
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 40700909-c8ae-405f-a4fb-7835cc2a5153 · outbound
Random approximate quantum information masking To simplify the above equation, we note that the operator |0⟩⟨0|−| v0⟩⟨v0| can be diagonalized by a unitary W as |0⟩⟨0|−| va⟩⟨va| =W p 1−a2|0⟩⟨0|− p 1−a2|1⟩⟨1| W†, (C13) then Eq
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b2dd8e29-fd8a-49ba-9716-c903d6c5c30f · outbound
Random approximate quantum information masking Using the results of Proposition 5, we can obtain eΛA B1(HB1B2) +eΛA B2(HB1B2)≥ 4− 1√d1 + 1√d2 4 (d12)1/2 d1X i=1 1/2 i 1/2 i− 1 (d2)3/2−i (d1 + 1)−i
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation bec3d68a-78c2-4dc6-982a-c6b97fe03b9d · outbound
Random approximate quantum information masking Here, according to Appendix B.4
Reference 68
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 93bafc66-df9e-4067-9d3c-51c46e37be00 · outbound
Random approximate quantum information masking Now, the proof of Theorem 2 is straightforward as follows
Reference 69
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 761b7818-9f03-48c4-b9b4-3122a02ad9b0 · outbound
Reference 70
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f277420c-07ac-480e-bf06-eb54250485b1 · outbound
Random approximate quantum information masking 2− 4√d1(d1d1)1/2 d1X i=1 1/2 i 1/2 i− 1 (d1)3/2−i (d1 + 1)−i # , (C46) v2 = (2dC− 2)(2d12− 1) (2dC− 1)(2d12− 2)
Reference 71
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d1f3f194-8b1d-4b89-9d45-905ab59e5840 · outbound
Random approximate quantum information masking Proposition 8
Reference 72
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0ab1b64c-ba53-4bb7-bf93-3ce01172a9bf · outbound
Random approximate quantum information masking Preparatory work: ϵ-net and Levy’s lemma To prove the results of this paper, we need to introduce two basic tools
Reference 73
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 090d8e32-7f1e-46fd-8e75-625ee15dd0b3 · outbound
Random approximate quantum information masking Unresolved cited work
Reference 74
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e3716482-0817-44cb-9a14-96e574bbfbff · outbound
Random approximate quantum information masking As in the proof of Theorem 5, we also fix a subspace HC0 in the Grassmannian Gr(HB1B2,dC) and transform the trace distance D(Π(B1) C ,e1B1) into a function of U ∈ SU(d12)
Reference 75
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2f54ef7a-08a2-4c5b-b142-5c6f14ad3ce3 · outbound
Random approximate quantum information masking Since eη(E,RS) =p dC(u +α), let γ :=k/m satisfy γ <1/2, then the parameter α becomes α = ˜η2 0 dC −u≈ ˜η2 0 dC −d(γ−1/2)m, (F1) where we have used the approximation u≈dk−m/2
Reference 76
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7e05cad8-a568-484a-894c-751adaf9f4c5 · outbound
Random approximate quantum information masking Since eη(E,RS) = p dC(u +α) with u≈dk−m/2, we assume the inaccuracy equals to da(k−m/2) with a> 0
Reference 77
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ff1a5ebb-9bd0-472b-9d9e-7e20de41f104 · inbound
Theory of approximate quantum error correction and the error-set model Random approximate quantum information masking
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.