Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-08T23:23:38.742822Z
Paper Citation Record · LEDGER
Cyclic quantum causal modelling with a graph separation theorem
As of 10 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 5 inbound Pith citation observations for arXiv:2502.04168.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-08T23:25:05.634003Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T04:59:36.773174Z
Reference resolution
29 of 29 outbound references displayed
- verified exact0
- verified fuzzy11
- unresolved18
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 05cd40fc-63a1-475f-8801-a20f5c622ce9 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.264169Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation fcb2cc98-dfb9-4f6e-beac-0e4b7aa82c9c · outbound
This paper cites Note that the original papers [BLO20, BLO21] useρAi|Pa(Ai) rather thanσAi|Pa(Ai) for the channels mentioned in the above definition.
Cyclic quantum causal modelling with a graph separation theorem Note that the original papers [BLO20, BLO21] useρAi|Pa(Ai) rather thanσAi|Pa(Ai) for the channels mentioned in the above definition
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.254368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 8fc88343-95af-459b-b0d8-ebf7620e4cb0 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.244517Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation b83c20c5-1b72-45be-aba8-73da16aef7ab · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.234483Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation dca45353-2573-46f6-8138-d5104266f4f6 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.224251Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation ef106ccc-3199-4a07-b567-580fd24f30ad · outbound
This paper cites We will use a notation where ifV′⊆V is a non-empty subset of vertices, XV′ = ∏ v∈V′ Xv (130) where∏here denotes the Cartesian product.
Cyclic quantum causal modelling with a graph separation theorem We will use a notation where ifV′⊆V is a non-empty subset of vertices, XV′ = ∏ v∈V′ Xv (130) where∏here denotes the Cartesian product
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.214369Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 192040f7-5c1d-4375-90a2-2f3237777422 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.204533Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 6a3c586f-d586-4b5a-b7a4-338effea4420 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.195174Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation afed5506-9965-4e1e-be05-7c40a59fb009 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.186542Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0f8a5aa6-57e4-4517-b399-bd136049265b · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.178031Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f80a7c14-7af9-406c-a876-4bbdaa63c42f · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.169918Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2668b37c-4e85-4d2a-8ed8-4940c7881f1c · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.160959Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 37cfa943-7d0f-447c-a971-a27d198d1c00 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.151481Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7b7154bc-9901-4260-ae6f-e69756beb53a · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.141886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2a68fddd-659a-48e5-9e38-3a57e382fb5f · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.131851Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation fa75f1bf-ff3b-458b-a9a0-ecfe39d00da6 · outbound
This paper cites Outgoing edges fromRi, (Ri,T i) and (Ri,v′ i), are quantum edges.
Cyclic quantum causal modelling with a graph separation theorem Outgoing edges fromRi, (Ri,T i) and (Ri,v′ i), are quantum edges
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.122011Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0d7600aa-d67a-4eff-b1c9-a95749dfa787 · outbound
This paper cites We refer toVs(Gc,tp) as the split vertices ofGc,tp.
Cyclic quantum causal modelling with a graph separation theorem We refer toVs(Gc,tp) as the split vertices ofGc,tp
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.112836Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation b1b98a2e-9f40-4a6b-af5a-1e22abce6276 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.103523Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation bb794755-b9e1-4ff1-bcda-e8a768e08021 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.094467Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2229807d-32e6-4211-b904-c961fd6f7fac · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.084495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 497ff8f0-9c0e-40fe-9ec6-90a333af9a59 · outbound
This paper cites Notice that this amounts to having the variable associated to pre-selection verticesRe v uniformly distributed (for more details see the remark in section 2 of [FGV25]).
Cyclic quantum causal modelling with a graph separation theorem Notice that this amounts to having the variable associated to pre-selection verticesRe v uniformly distributed (for more details see the remark in section 2 of [FGV25])
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.074298Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0cfa0832-fe07-4123-ae09-18d0df39ac69 · outbound
This paper cites Hence, each outgoing edge from a vertexv∈Vs(Gc,tp) in G has been replaced with a uniform prior classical teleportation protocol (definition 6 in [FGV25]).
Cyclic quantum causal modelling with a graph separation theorem Hence, each outgoing edge from a vertexv∈Vs(Gc,tp) in G has been replaced with a uniform prior classical teleportation protocol (definition 6 in [FGV25])
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.064183Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 30cf1613-d9fc-4441-9278-bf96457bb18d · outbound
This paper cites 24By construction, these are also the same association of the original causal modelfCmG on G.
Cyclic quantum causal modelling with a graph separation theorem 24By construction, these are also the same association of the original causal modelfCmG on G
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:39.053757Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9e97dd79-8efc-4fc9-9b20-bc31c8b7b811 · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:39.033474Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 310e88d2-8c62-4c7c-88c0-f89523731963 · outbound
This paper cites (177) Lemma 37 establishes that probabilities are preserved through mapping an acyclic functional model to an acyclic causal model through definition 36.
Cyclic quantum causal modelling with a graph separation theorem (177) Lemma 37 establishes that probabilities are preserved through mapping an acyclic functional model to an acyclic causal model through definition 36
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:38.973669Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f3a92908-05d1-40c5-8064-c468c4adbc5e · outbound
This paper cites an unresolved cited work.
Cyclic quantum causal modelling with a graph separation theorem Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T23:23:38.893528Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 3915240c-c4eb-4e56-a0c3-43ef478aa83c · outbound
This paper cites In order to evaluate probabili- ties, the maps ofCmGtp are composed as described in definition 3.
Cyclic quantum causal modelling with a graph separation theorem In order to evaluate probabili- ties, the maps ofCmGtp are composed as described in definition 3
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:38.803522Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 5ee0e136-9e3c-456e-acde-770acde0f291 · outbound
This paper cites 42= ˜Mv′ x′◦D (Rev,v′)◦ ˜σRe v (191) where˜denotes associations in CmGtp andD(Rev,v′) is a decohering channel.
Cyclic quantum causal modelling with a graph separation theorem 42= ˜Mv′ x′◦D (Rev,v′)◦ ˜σRe v (191) where˜denotes associations in CmGtp andD(Rev,v′) is a decohering channel
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:38.785454Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 073d380e-b4f3-47fe-a7ee-b10cf904ba39 · outbound
This paper cites D Proofs of section 4 Lemma 7(Acyclicity of teleportation graphs).
Cyclic quantum causal modelling with a graph separation theorem D Proofs of section 4 Lemma 7(Acyclicity of teleportation graphs)
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T23:23:38.774898Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Pith citing papers
Observation 7b1461ee-cd9d-413b-a6ac-ee277955e27c · inbound
Cyclic functional causal models beyond unique solvability with a graph separation theorem cites this paper.
Cyclic functional causal models beyond unique solvability with a graph separation theorem Cyclic quantum causal modelling with a graph separation theorem
Reference 1982
- Resolution
- unresolved
- no resolver link, observed 2026-08-08T23:25:05.634003Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e1c8887b-5f8e-46cb-afa6-066b499af255 · inbound
Events and their Localisation are Relative to a Lab cites this paper.
Events and their Localisation are Relative to a Lab Cyclic quantum causal modelling with a graph separation theorem
Reference 60
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T13:31:51.668618Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f573f19a-23dc-4fb4-a6ad-6d735f9c4d3c · inbound
An equivalence between time-symmetry and cyclic causality in quantum theory cites this paper.
An equivalence between time-symmetry and cyclic causality in quantum theory Cyclic quantum causal modelling with a graph separation theorem
Reference 46
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T05:17:00.885752Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 75c75ad1-bc2c-43ab-8513-a52658525713 · inbound
Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order cites this paper.
Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order Cyclic quantum causal modelling with a graph separation theorem
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T08:36:24.709663Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 15a399d6-b4d0-4227-80f1-6dbd6a7ee50c · inbound
Impossibility of superluminal signalling rules out causal loops in conical spacetimes cites this paper.
Impossibility of superluminal signalling rules out causal loops in conical spacetimes Cyclic quantum causal modelling with a graph separation theorem
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T04:59:36.775126Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.