Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T05:32:51.869295Z
Paper Citation Record · LEDGER
As of 23 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 0 inbound Pith citation observations for arXiv:2504.20732.
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 2026-08-16T05:32:51.869295Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
58 of 58 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 84b0fa26-4325-43dc-927a-8dc1e8ea1196 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bba5dac3-a2c7-4ad5-a9fe-c2972a33a39e · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5cf11f2c-5d01-414d-9e73-e9039b1e89b6 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e051cc46-cc1f-4884-95b8-2554941b3a35 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c693b7ee-7a79-4033-a63b-05524c3d4aa6 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d906d452-54b7-4613-9d20-62a0e04a2fba · outbound
Bayesian Inference in Quantum Programs ForS≡q := 0: We only show the case oftype(q) = Int, for Bool it is similar
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3cabd7b8-9115-4df8-99c5-94d54037c648 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f6172868-890d-4106-8d19-758a799a10ca · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 02ae1e48-c9fc-43fe-b101-f7088086868c · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 609a41f6-28a9-46e3-afe6-fcb71d39dc62 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d8fc1193-f1c8-49cf-8567-40b64bb52c93 · outbound
Bayesian Inference in Quantum Programs Ifρ is positive, then|0⟩⟨n|qρ|n⟩⟨ 0|q is positive
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3f1266a2-6ca0-40cf-97a8-89fcbe2fd47b · outbound
Bayesian Inference in Quantum Programs ForS≡q :=Uq:
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f6f73f38-f09e-4ec8-b4cd-8404c5827c9f · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e12819f7-a661-4274-a268-7377665e96a1 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c06c8aa5-815f-48be-9627-03ed9ba74366 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2fd8fc03-26c7-4d84-9c26-7b18d122b00d · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9d251bcd-6133-430d-a06a-088229e58039 · outbound
Bayesian Inference in Quantum Programs It istr(Jq :=UqKρ(ρ,p )) =tr(U†Uρ) =tr(ρ) and thustr(Jq :=UqKρ(ρ,p ))≤ 1
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation baa1add4-f9e9-4b73-976c-13c9fe9e88b2 · outbound
Bayesian Inference in Quantum Programs ForS≡ observe (¯q,O ):
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9fb3547f-e439-4d3b-8ff4-61f1931ea4d7 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6e4127a8-a31a-4bbd-b659-b479a6257bd6 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e00ed545-0200-4dd7-bb96-19e0cece2ccc · outbound
Bayesian Inference in Quantum Programs ˜tr(Jobserve (¯q,O )K(ρ,p )) =tr(Jobserve (¯q,O )Kρ(ρ,p )) +Jobserve (¯q,O )K (ρ,p ) =tr(OρO†) +p +tr(ρ)−tr(OρO†) =p +tr(ρ) = ˜tr(ρ,p ) C
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8bbaef65-9fe9-475e-b1f2-a1a7f48f7c5b · outbound
Bayesian Inference in Quantum Programs Also tr(Jobserve (¯q,O )Kρ(ρ,p )) = tr(O†Oρ) ≤ tr(ρ) ≤ 1
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 171e3700-c112-456b-95da-57c2b32661d6 · outbound
Bayesian Inference in Quantum Programs ForS≡S1;S2:
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 901891a6-3fbe-46be-aca1-076dc6695a01 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7db51648-4105-4cd8-9963-03dd7fcd90b5 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 173d3797-2473-4a39-a032-257a4a4b0431 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7a4d46ae-c82d-4f3e-b57b-e804fc04b49e · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3d65494f-2903-41bd-b402-c2acfe600d7b · outbound
Bayesian Inference in Quantum Programs We defineJS1;S2K : span(DR)→ span(DR) as JS1;S2K(ρ,p ) = (JS2K(JS1K(ρ,p ))) for (ρ,p )∈ span(DR) which is linear
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d5269178-067c-46a1-9194-8390dee1af51 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 51efa2cd-be96-484e-8701-4eac4a7b1ec4 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 09f8876d-3fad-4f67-a005-d15c08076a01 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9eee080b-582a-4b73-a1eb-bef4a88701a1 · outbound
Bayesian Inference in Quantum Programs It is Jmeasure M[¯q] : ¯S′Kρ(ρ,p ) = ∑ mJS′ mKρ(MmρM† m, 0) and JS′ mKρ(MmρM† m, 0) ∈ D−(H) for all m by induction hypothesis
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3dd5598a-a55b-4163-bfc4-4aaeb3fcbd53 · outbound
Bayesian Inference in Quantum Programs We defineJmeasure M[¯q] : ¯S′K : span(DR)→ span(DR) as Jmeasure M[¯q] : ¯S′K(ρ,p ) = ∑ mJS′mK(MmρM† m,p ) for (ρ,p )∈ span(DR) which is linear
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6b4ee646-06db-472a-bfe3-ab5bc379d1e2 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4f31ae32-c3f4-4c73-81d1-8f4450404651 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation fb0e8c40-666a-430d-8cfb-7c8e2b9325a8 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 090f6706-b905-4b15-bc96-68a7f29e54ed · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a60a580d-33a6-4ba9-8331-da4651cd8f8e · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation dff86584-5167-4604-b153-d1fbf180c54c · outbound
Bayesian Inference in Quantum Programs Gehnen, D
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b258f9f8-4e10-4d0e-91a3-3143a6d81533 · outbound
Bayesian Inference in Quantum Programs For all(ρ,p )∈DR is ˜tr(Jwhile M[¯q] = 1 do S′K(ρ,p ))≤ ˜tr(ρ,p )≤ 1 and Jwhile M[¯q] = 1 do S′K (ρ,p )≥ p≥ 0
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 38a9f847-83d3-4622-982e-7242489e1f52 · outbound
Bayesian Inference in Quantum Programs Note that we use thatJS′Kρ(ρ,p ) is independent ofp (property 1)
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8573ec23-b606-4e21-8abb-b1c1800015b1 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bf9e38b9-a8f1-4de8-aa90-0e31e9e88429 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 540df6e3-24fd-4ea3-84cb-d228d6d38c81 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 74ccbaba-131c-4915-bf58-afaf671fb7cc · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 33f8ac0f-8c49-486c-b23c-de7bc354ab84 · outbound
Bayesian Inference in Quantum Programs This is because for allρ∈D−(H) tr(Qρ)≤tr(PJSKρ(ρ, 0)) =tr(Pf (ρ)) =tr(g(P )ρ) which meansQ⊑g(P ) [27]
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2106d3de-89cf-4fea-8a40-6a299e5bdc71 · outbound
Bayesian Inference in Quantum Programs = tr(qwpJSK(P )ρ)−tr(qwpJSK(I)ρ) +tr(Iρ)−tr(1·f(ρ)) def f = tr(PJSK(ρ))−tr(IJSK(ρ)) +tr(ρ)−tr(1·JSK (ρ, 0)) = tr(PJSK(ρ))−tr(JSK(ρ)) +tr(ρ)−JSK (ρ, 0)
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 65bc76a9-ff05-4338-af9c-da87b1a4ca96 · outbound
Bayesian Inference in Quantum Programs This is because for all ρ∈D−(H) tr(Qρ)≤tr(PJSK(ρ))−tr(JSK(ρ)) +tr(ρ)−JSK (ρ, 0) =tr(qwlpJSK(P )ρ) so Q⊑qwlpJSK(P )
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 569c513d-e0dd-4486-87eb-61c89005e0f8 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 45ca0ca7-d4e6-41e4-a747-af30c4e87f85 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b2f2ba3d-affd-4cb2-9fc9-a1d451fc4ba1 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4cd1e766-843b-4ec1-8ee3-3b9fae1d8588 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 99423c6a-b3ef-4eac-b5aa-3b25aed9ea87 · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 17318b54-4673-4f96-a84d-2ea555788f3b · outbound
Bayesian Inference in Quantum Programs Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f0bb0bb2-f7cc-4035-86fb-0a7c2ba72ac9 · outbound
Bayesian Inference in Quantum Programs Gehnen, D
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation fd2da0e5-ec5c-47bd-9ea8-3e4edca7b3db · outbound
Bayesian Inference in Quantum Programs Optimal Discrete Uniform Generation from Coin Flips, and Applications
Reference 1985
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 454d39dd-2506-4f50-8653-941c52312043 · outbound
Bayesian Inference in Quantum Programs 2 Christel Baier and Joost-Pieter Katoen.Principles of model checking
Reference 2005
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 25c9b8aa-0e9b-48b1-b3bd-62b9e52e3bec · outbound
Bayesian Inference in Quantum Programs 28 Mingsheng Ying, Runyao Duan, Yuan Feng, and Zhengfeng Ji
Reference 2012
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
No inbound Pith citation observations are available.