Paper Citation Record · LEDGER

On the saturated cases of the distillability conjecture

As of 22 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 2 inbound Pith citation observations for arXiv:2606.03561.

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

pith.paper-citation-record.v1
2606.03561 v1

Coverage vector

measured 68 of 68 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T09:27:14.693975Z

measured 70 of 70 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T07:49:51.266776Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

68 of 68 outbound references displayed

verified exact0
verified fuzzy0
unresolved66
parse uncertain2
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6b23a34a-3a29-4574-ad36-21f967d1637e · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation e317aee1-b447-4e4e-950e-13f0254b1a47 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 2

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Observation f5ed1a38-58da-4376-921d-e6f3528f96a2 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 3

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Observation 56012bb9-59f4-45ad-a84e-d5ebe22ddf02 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 4

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Observation 6464a680-5020-4963-ab6d-8f1610989948 · outbound

This paper cites [ 17] Definition 3.

On the saturated cases of the distillability conjecture [ 17] Definition 3

Reference 5

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Observation e4efee0c-83d9-4fc0-badf-78498c4b0718 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 753e535a-4e39-49c8-998f-d72a04a10b68 · outbound

This paper cites (10) Lemma 6.

On the saturated cases of the distillability conjecture (10) Lemma 6

Reference 7

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Observation 896c1a18-9531-470a-a3c2-89fdbb7ccbd5 · outbound

This paper cites Inequality (4) is saturated if and only if rank A = 1.

On the saturated cases of the distillability conjecture Inequality (4) is saturated if and only if rank A = 1

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 94d2220b-b176-43c8-8c03-35d3176b8855 · outbound

This paper cites Inequality (4) is saturated if and only if rank B = 1.

On the saturated cases of the distillability conjecture Inequality (4) is saturated if and only if rank B = 1

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 27c92051-f133-4117-835a-c7aa265e0473 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 8b3c6a3e-98d5-4a80-9894-4e49a5900be6 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 11

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Observation 52fc1f31-d6c7-4b5c-8ec8-8076544d3e8c · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 12

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Observation 1baa6551-3550-444a-ad7f-c56318bd9cac · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 13

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Observation b73306f4-a4cd-4116-b0a8-86600b36201d · outbound

This paper cites 4 Part 1, 2, 3, 4, 5, and 7 of the theorem are respectively supported by Lemma 8, 9, 10, 11, 12, and 15.

On the saturated cases of the distillability conjecture 4 Part 1, 2, 3, 4, 5, and 7 of the theorem are respectively supported by Lemma 8, 9, 10, 11, 12, and 15

Reference 14

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Observation 1f47bb04-b0be-40fd-a6ef-cfc22e7bf3c2 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 16

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Observation c7593223-d749-450d-9ffb-787ec437e344 · outbound

This paper cites According to equation (53c) of [ 15], σ2 1(X) + σ2 2(X) = 1 2 only if A and B are both normal.

On the saturated cases of the distillability conjecture According to equation (53c) of [ 15], σ2 1(X) + σ2 2(X) = 1 2 only if A and B are both normal

Reference 17

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Observation cc4a70af-828f-4a70-827f-f1ecb99309c0 · outbound

This paper cites According to Lemmas 18 and 19 of [ 15], σ2 1(X) + σ2 2(X) = 1 2 only if A is normal and B is 2 2 block-diagonal.

On the saturated cases of the distillability conjecture According to Lemmas 18 and 19 of [ 15], σ2 1(X) + σ2 2(X) = 1 2 only if A is normal and B is 2 2 block-diagonal

Reference 18

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Observation da0d80a7-330a-419e-abd1-021157349cf5 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 19

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Observation 1f230c98-9fc6-4312-8054-d7847e74ee3b · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 20

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Observation 0941faa2-c427-4858-a2fe-63ec69d1f244 · outbound

This paper cites From these conditions the conclusion follows.

On the saturated cases of the distillability conjecture From these conditions the conclusion follows

Reference 21

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Observation 35e78543-c241-4ce2-9c00-f431b9ac731e · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 22

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Observation 373b7f11-5cab-4cf1-b4ec-9823a6bd0629 · outbound

This paper cites We can see that in the first case, A is necessarily 2 2 block-diagonal, and so is B.

On the saturated cases of the distillability conjecture We can see that in the first case, A is necessarily 2 2 block-diagonal, and so is B

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 162040c8-d79f-4d57-b58e-f2d0deacf5fb · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation cffc0fec-656d-494d-8490-4d4a053c3f0f · outbound

This paper cites Lemma 21.

On the saturated cases of the distillability conjecture Lemma 21

Reference 25

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Observation 06fbf283-f6c2-4c8d-8059-0d4f68e1b361 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 27

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Observation 85603f12-7424-4444-9683-af6eb53169eb · outbound

This paper cites (29) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3355, 0.3355, 0.2821, 0.2821, 0.1841, 0.1841, 0.1548, 0.1548, 0, , 0].

On the saturated cases of the distillability conjecture (29) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3355, 0.3355, 0.2821, 0.2821, 0.1841, 0.1841, 0.1548, 0.1548, 0, , 0]

Reference 28

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Observation 3eb17751-1287-45a4-8a68-f08a4c964353 · outbound

This paper cites (31) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.4251, 0.4251, 0.2632, 0.2632, 0.0044, 0.0044, 0.0027, 0.0027, 0, , 0].

On the saturated cases of the distillability conjecture (31) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.4251, 0.4251, 0.2632, 0.2632, 0.0044, 0.0044, 0.0027, 0.0027, 0, , 0]

Reference 29

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Observation 41fe3b05-9d7d-404d-af63-b9fe515393ce · outbound

This paper cites (33) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3996, 0.3996, 0.2003, 0.2003, 0.2003, 0.2003, 0.1004, 0.1004, 0, , 0].

On the saturated cases of the distillability conjecture (33) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3996, 0.3996, 0.2003, 0.2003, 0.2003, 0.2003, 0.1004, 0.1004, 0, , 0]

Reference 30

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Observation 80b3f0d6-be9c-44eb-8cc4-f26cb4c2c792 · outbound

This paper cites (35) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3586, 0.3586, 0.3001, 0.3001, 0.1358, 0.1358, 0.1137, 0.1137, 0, , 0].

On the saturated cases of the distillability conjecture (35) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3586, 0.3586, 0.3001, 0.3001, 0.1358, 0.1358, 0.1137, 0.1137, 0, , 0]

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 6506067c-153f-45ad-9bed-f72b18f2552b · outbound

This paper cites (37) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3172, 0.3172, 0.2408, 0.2408, 0.2408, 0.2408, 0.1828, 0.1828, 0, , 0].

On the saturated cases of the distillability conjecture (37) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3172, 0.3172, 0.2408, 0.2408, 0.2408, 0.2408, 0.1828, 0.1828, 0, , 0]

Reference 32

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Observation 3bcfe5e7-7450-49c4-a240-cac05ce58418 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 33

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Observation 75bfd2dc-33c4-429d-b014-64fcfbd580f8 · outbound

This paper cites In case 1, we claim that a1 = b1 = a2 = b2, ja1j = jb1j = ja2j = jb2j = 1 4 and b3 = b4 = a3 = a4 = 0.

On the saturated cases of the distillability conjecture In case 1, we claim that a1 = b1 = a2 = b2, ja1j = jb1j = ja2j = jb2j = 1 4 and b3 = b4 = a3 = a4 = 0

Reference 34

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Observation f3c2d813-d329-4c05-bb1c-953a18d17a16 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 35

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Observation ec9105fe-260a-4f09-8ab2-e62adbb432f1 · outbound

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On the saturated cases of the distillability conjecture Unresolved cited work

Reference 37

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Observation 721339d2-e01f-4529-b390-ce666d2e3e48 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 38

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Observation 8157d706-f207-4251-9752-64bf8e3bbfa7 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 39

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Observation e0cd520b-a1bb-4460-87ec-677ee58b3bcf · outbound

This paper cites We can verify that all of the three cases above saturate the original conjecture.

On the saturated cases of the distillability conjecture We can verify that all of the three cases above saturate the original conjecture

Reference 40

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Observation 199760a8-642a-43e5-aa02-e37f18f4464b · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 41

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Observation f9125981-e010-4862-a9c5-2d130718533b · outbound

This paper cites Z11 (11) Z11 (12) Z11 (12)∗ Z11 (22) # , Z 22 = Y22Y22 ∗ =.

On the saturated cases of the distillability conjecture Z11 (11) Z11 (12) Z11 (12)∗ Z11 (22) # , Z 22 = Y22Y22 ∗ =

Reference 42

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Observation 0a96e221-96e0-4148-bb2d-b6052dcad904 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 43

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Observation 75e0efd6-253f-4878-b772-e6a0bd906401 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 2b62e0c6-e547-4398-a4fe-a95412524922 · outbound

This paper cites W e first deal with case 1.

On the saturated cases of the distillability conjecture W e first deal with case 1

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation f170f253-3a96-4842-9eb3-48e81c31f9ce · outbound

This paper cites (C33) The corresponding maximum eigenvector is a1 b2.

On the saturated cases of the distillability conjecture (C33) The corresponding maximum eigenvector is a1 b2

Reference 46

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 507300a5-2ed5-4f2b-9adc-0a136aaea4c6 · outbound

This paper cites Five open problems in quantum information theory.

On the saturated cases of the distillability conjecture Five open problems in quantum information theory

Reference 47

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation f02325bd-bcf0-4976-9f44-7ece991ac7d0 · outbound

This paper cites Inseparable two spin- 1 2 density matrices can be distilled to a singlet form.

On the saturated cases of the distillability conjecture Inseparable two spin- 1 2 density matrices can be distilled to a singlet form

Reference 48

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Unavailable: canonical work link unavailable.

Observation 38943985-e5a2-426e-890e-a3ebf4af835e · outbound

This paper cites Horodecki and P.

On the saturated cases of the distillability conjecture Horodecki and P

Reference 49

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation ad9f74a3-65b7-4c63-9b2e-263b05b2c8a4 · outbound

This paper cites Kraus, M.

On the saturated cases of the distillability conjecture Kraus, M

Reference 50

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Observation c01e13bf-4d54-422f-a28f-660fbec73e4f · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 51

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Observation b7659e7b-1b71-4340-9dad-f7d787514dc6 · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 52

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Observation 0ffa75f8-4f15-48b8-98d7-c9a1474fe20e · outbound

This paper cites an unresolved cited work.

On the saturated cases of the distillability conjecture Unresolved cited work

Reference 53

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Unavailable: canonical work link unavailable.

Observation d83515c4-1154-4756-8244-e30ed1aaba8b · outbound

This paper cites Classes of n-copy undistillable quantum states with negative partial transposition.

On the saturated cases of the distillability conjecture Classes of n-copy undistillable quantum states with negative partial transposition

Reference 54

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 4db2b033-e39e-469c-89fd-60d7345d3539 · outbound

This paper cites Devetak and A.

On the saturated cases of the distillability conjecture Devetak and A

Reference 55

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Observation 8e7c8dcc-5b2f-4453-a972-a270da7b237f · outbound

This paper cites Vianna and Andrew C.

On the saturated cases of the distillability conjecture Vianna and Andrew C

Reference 56

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation d48c3595-75c2-4b22-9f75-e674646c753d · outbound

This paper cites Distillability and ppt entanglement of low-rank quantum states.

On the saturated cases of the distillability conjecture Distillability and ppt entanglement of low-rank quantum states

Reference 57

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Unavailable: canonical work link unavailable.

Observation f530b472-e71b-4c99-8788-2bb900178778 · outbound

This paper cites Rank-three bipartite entangled states are distillable.

On the saturated cases of the distillability conjecture Rank-three bipartite entangled states are distillable

Reference 58

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 3f48021c-e033-4525-a25f-ea2b2144ef4c · outbound

This paper cites Distillability of non-positive-partial-transpose bipartite quantum states of rank four.

On the saturated cases of the distillability conjecture Distillability of non-positive-partial-transpose bipartite quantum states of rank four

Reference 59

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation ff0efc84-120e-4c53-bac2-0e3ffffca5c1 · outbound

This paper cites A few steps more towards npt bound entangle- ment.

On the saturated cases of the distillability conjecture A few steps more towards npt bound entangle- ment

Reference 60

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Observation 2a42bcfc-48f0-46e2-ad80-3fb0bf653847 · outbound

This paper cites A matrix inequality for entanglement distillation problem.

On the saturated cases of the distillability conjecture A matrix inequality for entanglement distillation problem

Reference 61

Resolution: unresolved; no resolver link, observed 2026-06-28T09:27:14.693975Z

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Unavailable: canonical work link unavailable.

Observation 39be44d0-986b-41c5-ab06-7273b076119c · outbound

This paper cites On the distillability conjecture in matrix theory.

On the saturated cases of the distillability conjecture On the distillability conjecture in matrix theory

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Observation b41cb2b1-691f-49a6-a815-0dbb28ec36c2 · outbound

This paper cites A note on a conjecture from distillability of quantum entanglement.

On the saturated cases of the distillability conjecture A note on a conjecture from distillability of quantum entanglement

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This paper cites Proving the distillability problem of two-copy 4 × 4 werner states for monomial matrices.

On the saturated cases of the distillability conjecture Proving the distillability problem of two-copy 4 × 4 werner states for monomial matrices

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This paper cites On some norm inequalities involving the commutator and xy-yxt.

On the saturated cases of the distillability conjecture On some norm inequalities involving the commutator and xy-yxt

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Observation 9613cb57-2459-4401-a339-356efc965c2c · outbound

This paper cites Commutators with maximal frobenius norm.

On the saturated cases of the distillability conjecture Commutators with maximal frobenius norm

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Observation 71e40a0d-bce9-4c57-aecf-d0b6f1e600c6 · outbound

This paper cites Michel and B.I.

On the saturated cases of the distillability conjecture Michel and B.I

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On the saturated cases of the distillability conjecture Unresolved cited work

Reference 68

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This paper cites On the periodicity of singular vectors and the holomorphic block-circulant svd on the unit circum- ference.

On the saturated cases of the distillability conjecture On the periodicity of singular vectors and the holomorphic block-circulant svd on the unit circum- ference

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This paper cites Differentiability of a function and of its compositions with functions of one variable.

On the saturated cases of the distillability conjecture Differentiability of a function and of its compositions with functions of one variable

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This paper cites Horn and Charles R.

On the saturated cases of the distillability conjecture Horn and Charles R

Reference 71

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Pith citing papers

Observation 43dd4031-b0aa-4699-884f-415b18f94800 · inbound

A solution to 2-copy distillability of Werner states cites this paper.

A solution to 2-copy distillability of Werner states On the saturated cases of the distillability conjecture

Reference 21

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Two-copy nondistillability of Werner states: sharp partial-trace inequalities and finite-copy extensions cites this paper.

Two-copy nondistillability of Werner states: sharp partial-trace inequalities and finite-copy extensions On the saturated cases of the distillability conjecture

Reference 15

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