Paper Citation Record · LEDGER

Every PPT channel has finite entanglement-breaking index

As of 15 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2608.13551.

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

pith.paper-citation-record.v1
2608.13551 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T04:33:31.585876Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact5
verified fuzzy28
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 251971c5-ac3f-4aa2-8de4-9ae6b61abb79 · outbound

This paper cites Beyond the Positive Partial Transpose Squared Conjecture: The Qutrit Case.

Every PPT channel has finite entanglement-breaking index Beyond the Positive Partial Transpose Squared Conjecture: The Qutrit Case

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:33:32.016623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d5620db2-3e22-4f36-877b-fa110825d5e1 · outbound

This paper cites Completely positive linear maps on complex matrices.

Every PPT channel has finite entanglement-breaking index Completely positive linear maps on complex matrices

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.478440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c6eeeffc-f1eb-4956-a06c-d2259eedd9d2 · outbound

This paper cites an unresolved cited work.

Every PPT channel has finite entanglement-breaking index Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-14T04:33:33.307544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 97c73c9d-7f28-42cc-99dc-b2cbf4231463 · outbound

This paper cites Positive-partial-transpose square conjecture for n= 3.

Every PPT channel has finite entanglement-breaking index Positive-partial-transpose square conjecture for n= 3

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.280227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 366f6862-5d2d-4995-8b72-a9bd4f5921cf · outbound

This paper cites Mapping cone of k-entanglement breaking maps.

Every PPT channel has finite entanglement-breaking index Mapping cone of k-entanglement breaking maps

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.268357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 39863fbb-97e0-47ce-8e09-87bc47536d76 · outbound

This paper cites Spectral properties of positive maps on c*-algebras.

Every PPT channel has finite entanglement-breaking index Spectral properties of positive maps on c*-algebras

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.252313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 47acae76-8dc1-4b90-a0ad-4a2b8950d01d · outbound

This paper cites Convex cones in mapping spaces between matrix algebras.

Every PPT channel has finite entanglement-breaking index Convex cones in mapping spaces between matrix algebras

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.218473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a8f03db9-9ffb-4696-a48a-cad0fde028ac · outbound

This paper cites Ppt composition through a qubit is entanglement breaking.

Every PPT channel has finite entanglement-breaking index Ppt composition through a qubit is entanglement breaking

Reference 8

Resolution: verified exact; doi, observed 2026-08-14T04:33:31.616855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fdfc7024-1912-4025-9d33-4d9747c3eb86 · outbound

This paper cites Reduction criterion of separability and limits for a class of distillation protocols.

Every PPT channel has finite entanglement-breaking index Reduction criterion of separability and limits for a class of distillation protocols

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.120189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ce2dd622-7036-4ee2-8bc5-7bdba132a5c6 · outbound

This paper cites Separability of mixed states: necessary and sufficient conditions.

Every PPT channel has finite entanglement-breaking index Separability of mixed states: necessary and sufficient conditions

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.080148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7e2376a3-e436-4db4-a039-32e57ff8d70f · outbound

This paper cites Mixed-state entanglement and distillation: Is there a “bound” entanglement in nature? Physical Review Letters , 80(24):5239, 1998.

Every PPT channel has finite entanglement-breaking index Mixed-state entanglement and distillation: Is there a “bound” entanglement in nature? Physical Review Letters , 80(24):5239, 1998

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.069494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6f7e3d06-44aa-4b8f-b4bb-294ce8605c8e · outbound

This paper cites Quantum systems, channels, information: a mathematical introduction.

Every PPT channel has finite entanglement-breaking index Quantum systems, channels, information: a mathematical introduction

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.058345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 26c8c492-3a66-4d1d-9253-4e788345ad94 · outbound

This paper cites Eventually entanglement breaking markovian dynamics: Structure and characteristic times: Ep hanson et al.

Every PPT channel has finite entanglement-breaking index Eventually entanglement breaking markovian dynamics: Structure and characteristic times: Ep hanson et al

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.046842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7c8ff143-eff1-4284-81ef-cd447d2ec258 · outbound

This paper cites Shor, and Mary Beth Ruskai.

Every PPT channel has finite entanglement-breaking index Shor, and Mary Beth Ruskai

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:33.034535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4640c29d-59b8-462d-845c-57e3ee406812 · outbound

This paper cites Jamio kowski.

Every PPT channel has finite entanglement-breaking index Jamio kowski

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.927810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1eb15176-e8f4-4978-a59e-df20c7d88b2c · outbound

This paper cites Composition of PPT Maps.

Every PPT channel has finite entanglement-breaking index Composition of PPT Maps

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:33:31.909448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 902dcaae-dcd5-47f4-8fd1-1b68276ee520 · outbound

This paper cites Compositions and tensor products of linear maps between matrix algebras.

Every PPT channel has finite entanglement-breaking index Compositions and tensor products of linear maps between matrix algebras

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.858225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation afff4f8f-aadb-4216-a16e-2a354b02b8fb · outbound

This paper cites Positive maps in quantum information theory.

Every PPT channel has finite entanglement-breaking index Positive maps in quantum information theory

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.847299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 85f890b1-bf4b-4dc1-bb64-7d3105b306b0 · outbound

This paper cites Entanglement--breaking indices.

Every PPT channel has finite entanglement-breaking index Entanglement--breaking indices

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.826141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a4122e6a-2475-4b46-96a1-50781b37ea87 · outbound

This paper cites Entanglement-saving channels.

Every PPT channel has finite entanglement-breaking index Entanglement-saving channels

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.702188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6a85b809-f556-4bac-a4c1-c57b57bfc227 · outbound

This paper cites Nielsen and Isaac L.

Every PPT channel has finite entanglement-breaking index Nielsen and Isaac L

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-14T04:33:31.364723Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dcdaf7d7-fb8f-4a7f-8180-23a4b6bef9d9 · outbound

This paper cites Random covariant quantum channels: I.

Every PPT channel has finite entanglement-breaking index Random covariant quantum channels: I

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.588801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d435e357-2a66-4402-a2cb-6752ad08a916 · outbound

This paper cites k -positivity and high-dimensional bound entanglement under symplectic group symmetries.

Every PPT channel has finite entanglement-breaking index k -positivity and high-dimensional bound entanglement under symplectic group symmetries

Reference 23

Resolution: verified exact; raw_fallback, observed 2026-08-14T04:33:31.758669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f2226588-909b-4d10-b983-30da70971133 · outbound

This paper cites Separability criterion for density matrices.

Every PPT channel has finite entanglement-breaking index Separability criterion for density matrices

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.580457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 10f709da-bc74-48da-8c81-bd74c7edaa0c · outbound

This paper cites Entanglement Breaking Structure of Cartan-Covariant Quantum Channels.

Every PPT channel has finite entanglement-breaking index Entanglement Breaking Structure of Cartan-Covariant Quantum Channels

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:33:31.632967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 76887bfc-a91a-46a5-965f-65e20ee1eb5d · outbound

This paper cites k-positivity and schmidt number under orthogonal group symmetries.

Every PPT channel has finite entanglement-breaking index k-positivity and schmidt number under orthogonal group symmetries

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.547635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 56c54ada-1abd-4f63-a238-e5d54b56ead3 · outbound

This paper cites Eventually entanglement breaking maps.

Every PPT channel has finite entanglement-breaking index Eventually entanglement breaking maps

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.471754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3e63a921-f44d-459a-9897-334b3225b07c · outbound

This paper cites The ppt 2 conjecture holds for all choi-type maps.

Every PPT channel has finite entanglement-breaking index The ppt 2 conjecture holds for all choi-type maps

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.382926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a2a0fc4d-49f7-41ec-871f-0c7e5d41d0c9 · outbound

This paper cites Extension of positive maps into B( H ).

Every PPT channel has finite entanglement-breaking index Extension of positive maps into B( H )

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.370382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 90558525-8a12-4811-ac93-41ea1d3fb749 · outbound

This paper cites Z yczkowski.

Every PPT channel has finite entanglement-breaking index Z yczkowski

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.335849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9f2f071f-edb2-4369-95c3-086e5f7b0259 · outbound

This paper cites Terhal and Pawe Horodecki.

Every PPT channel has finite entanglement-breaking index Terhal and Pawe Horodecki

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.252407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2d273555-884f-4b30-8886-809094949d8a · outbound

This paper cites On the geometry of positive maps in matrix algebras.

Every PPT channel has finite entanglement-breaking index On the geometry of positive maps in matrix algebras

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.127209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 77f8318c-63bb-4541-8dc4-1262a538f825 · outbound

This paper cites an unresolved cited work.

Every PPT channel has finite entanglement-breaking index Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-14T04:33:32.117168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7efaffa0-03d3-4382-aab8-ac46668991fe · outbound

This paper cites Quantum channels and operations-guided tour.

Every PPT channel has finite entanglement-breaking index Quantum channels and operations-guided tour

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.092552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8899f690-70e5-490b-a0aa-bd195816f708 · outbound

This paper cites Extremals and exposed faces of the cone of positive maps.

Every PPT channel has finite entanglement-breaking index Extremals and exposed faces of the cone of positive maps

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.083027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0b15a1a1-95fa-4881-b07e-752e4c99f792 · outbound

This paper cites Leung, and Wai-Shing Tang.

Every PPT channel has finite entanglement-breaking index Leung, and Wai-Shing Tang

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:33:32.047609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.