Paper Citation Record · LEDGER

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states

As of 9 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2506.23727.

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

pith.paper-citation-record.v1
2506.23727 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:45:21.678407Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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 fuzzy12
unresolved18
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 56228425-2f5a-4924-99e0-2b2e478065ef · outbound

This paper cites Einstein, B.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Einstein, B

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:17.383008Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 176c1b29-af6d-4910-94d9-c7a1b2befe6c · outbound

This paper cites We consider here through eq.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states We consider here through eq

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:27.211133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d9a1c4d3-6718-405e-bc22-580e567bde0e · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:17.490666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9334baab-9704-4a84-afa9-b13c554ce45d · outbound

This paper cites Horodecki, P.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Horodecki, P

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:17.561405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98fcdc1b-fecc-4ce6-a047-ce99267ad45c · outbound

This paper cites G¨ uhne and G.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states G¨ uhne and G

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:27.053011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0f8eaf55-d787-4fcc-8ea5-66a04138c6da · outbound

This paper cites Gurvits, Classical deterministic complexity of edmonds’ problem and quantum entanglement (2003), arXiv:quant- ph/0303055 [quant-ph].

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Gurvits, Classical deterministic complexity of edmonds’ problem and quantum entanglement (2003), arXiv:quant- ph/0303055 [quant-ph]

Reference 6

Resolution: verified exact; raw_fallback, observed 2026-08-06T21:45:23.141432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ea730f43-8054-4dcc-af78-940b4bcef7cc · outbound

This paper cites Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Physics Letters A232, 333–339 (1997).

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Physics Letters A232, 333–339 (1997)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:26.949004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1b82ae49-6df9-4d91-a12b-f680c0330a62 · outbound

This paper cites Horodecki and P.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Horodecki and P

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:26.766419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7adb424f-9c2d-4b0e-8fdb-b60e5a84ddc0 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:26.614114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 525ae989-95c1-49dc-a29a-dfc0e2ab370f · outbound

This paper cites G¨ uhne, P.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states G¨ uhne, P

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:26.423012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 87e77e01-fafb-4a8f-919c-c82d6e8c1910 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:26.274769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bf9b27a8-4deb-4965-9e6e-41563090d313 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:26.112737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fbbdcfa0-a625-442c-b0f1-a049d903fa10 · outbound

This paper cites Dutta, B.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Dutta, B

Reference 13

Resolution: verified exact; doi, observed 2026-08-06T21:45:21.921770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6161deaa-1c4a-42d2-bc49-a56eca7fbfe3 · outbound

This paper cites Peres, Separability criterion for density matrices, Phys.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Peres, Separability criterion for density matrices, Phys

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:18.607815Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8ad1550e-146e-41cb-ac12-64df4a2e7091 · outbound

This paper cites Horodecki, P.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Horodecki, P

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:25.963040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2c36b4b8-2d14-4b0a-b079-c92ca4ed76e2 · outbound

This paper cites Rudolph, Some properties of the computable cross-norm criterion for separability, Phys.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Rudolph, Some properties of the computable cross-norm criterion for separability, Phys

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:25.802787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 32965350-75be-4e41-bcde-231730d7c88a · outbound

This paper cites A matrix realignment method for recognizing entanglement.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states A matrix realignment method for recognizing entanglement

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:18.938221Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4458ad98-afaf-442b-b24e-98320e53f8b5 · outbound

This paper cites A few entanglement criterion for two-qubit and two-qudit system based on realignment operation.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states A few entanglement criterion for two-qubit and two-qudit system based on realignment operation

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:45:22.877096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8407250f-a2eb-48b1-8b16-acd10e61b1f2 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:25.647113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2432c053-b9bf-47f0-9188-9b992b6d50b1 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:19.343715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e62d423-9f4e-420d-a419-b664f471aa67 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T21:45:19.490586Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf653cda-59e8-446f-acc7-db66829b5d87 · outbound

This paper cites Ishizaka and T.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Ishizaka and T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:25.415634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c8b72989-f014-4a21-b262-fbd86942798b · outbound

This paper cites Verstraete, K.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Verstraete, K

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:25.207215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8962256d-cdcf-4a4f-bb23-f40835ef5c55 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:24.987350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 23e45709-8139-4a2b-a93a-337224b82cc5 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:24.835308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation adedb6c7-5a97-4a60-bd39-4246c4788039 · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:24.684350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7b5db235-ddac-47de-a92d-29f9750b7107 · outbound

This paper cites Quesada, A.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Quesada, A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:24.547560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 248f11a2-ace2-4783-9a10-946845a14eda · outbound

This paper cites Evidence that All States Are Unitarily Equivalent to X States of the Same Entanglement.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Evidence that All States Are Unitarily Equivalent to X States of the Same Entanglement

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:45:22.719619Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 83ceca50-167f-491c-badb-d74905751c70 · outbound

This paper cites Generalized discord, entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: Hierarchy of quantum resources and chronology of deaths and births.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Generalized discord, entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: Hierarchy of quantum resources and chronology of deaths and births

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-06T21:45:22.508264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 66bec330-59ae-45c8-9fa3-824831237a7d · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:24.281006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation af4e325d-d9e9-4b28-8f35-501f91dbc0bb · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:24.108775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 414cba30-83d6-4000-9630-e1e98c11007f · outbound

This paper cites Barbieri, F.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Barbieri, F

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:23.862077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f0addbe9-1878-4e1a-b80d-45c1ade482e0 · outbound

This paper cites Cinelli, G.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Cinelli, G

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:45:23.644943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 892d5a07-0216-4fa8-877d-7567c54121ab · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:23.465003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c7e27c10-49ab-4118-8d29-4ca7f4b8f45b · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:45:23.303216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 020dcdaf-10d9-4c49-95e4-a41b50f4ae8b · outbound

This paper cites an unresolved cited work.

Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states Unresolved cited work

Reference 38

Resolution: malformed identifier; no resolver link, observed 2026-08-06T21:45:21.678407Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.