Hierarchy of entanglement detection criteria for random high-dimensional states | Paper Citation Record

Observation f1ed06e1-d510-4a06-81f6-adbb7bd0f16d · outbound

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Observation 0c53651c-3c37-4d07-a400-af98017a075a · outbound

This paper cites ,l(m), for two lists x, and y, containing l and m elements respectively ar- ranged in descending order.

Hierarchy of entanglement detection criteria for random high-dimensional states ,l(m), for two lists x, and y, containing l and m elements respectively ar- ranged in descending order

Reference 2

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Observation 80238684-14ba-41de-9b09-a01294f11b0a · outbound

This paper cites Using the relation between the Frobenius norm, ∥·∥F [97, 100], and the trace norm, we can write ρRl 12 1 ≤ d1 ρRl 12 F , where, ∥·∥F = q ∑i,j |aij |2 for a matrix with elements aij.

Hierarchy of entanglement detection criteria for random high-dimensional states Using the relation between the Frobenius norm, ∥·∥F [97, 100], and the trace norm, we can write ρRl 12 1 ≤ d1 ρRl 12 F , where, ∥·∥F = q ∑i,j |aij |2 for a matrix with elements aij

Reference 3

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Observation 3f1c80a5-1836-4458-a0b7-cbfa971b6985 · outbound

This paper cites ,l(m), for two lists x, and y, containing l and m elements re- spectively arranged in descending order.

Hierarchy of entanglement detection criteria for random high-dimensional states ,l(m), for two lists x, and y, containing l and m elements re- spectively arranged in descending order

Reference 4

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Observation 4caab63e-b458-4c69-be4d-ac7d4f43b1a7 · outbound

This paper cites We focus exclusively on states that are entan- gled under the partial transposition criterion, i.e., only non-positive partial transpose (NPT) states are consid- ered.

Hierarchy of entanglement detection criteria for random high-dimensional states We focus exclusively on states that are entan- gled under the partial transposition criterion, i.e., only non-positive partial transpose (NPT) states are consid- ered

Reference 5

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Observation eda577c5-123d-45d5-abe9-6eacd4a0994d · outbound

This paper cites Each mixed state is obtained by tracing out the third subsystem from a random pure state, |ψ⟩123 = ∑l,m,k(almk + iblmk ) |l⟩1 ⊗ |m⟩2 ⊗ |k⟩3, defined on d1 ⊗ d2 ⊗ k.

Hierarchy of entanglement detection criteria for random high-dimensional states Each mixed state is obtained by tracing out the third subsystem from a random pure state, |ψ⟩123 = ∑l,m,k(almk + iblmk ) |l⟩1 ⊗ |m⟩2 ⊗ |k⟩3, defined on d1 ⊗ d2 ⊗ k

Reference 6

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Observation c2a544e1-e678-47c1-afae-e10570414a65 · outbound

This paper cites does the efficiency of the entanglement detection method depend on the amount of entanglement possessed by random quantum states?.

Hierarchy of entanglement detection criteria for random high-dimensional states does the efficiency of the entanglement detection method depend on the amount of entanglement possessed by random quantum states?

Reference 7

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Observation 944bb64b-ce5a-47dd-8a97-f405cf738bd0 · outbound

This paper cites The PT, ρT1 12, of ρ12 with respect to the subsystem 1, is defined as ρT1 12 = ∑ 1≤i,j≤d1 ∑ 1≤µ,ν≤d2 aµν ij (|j⟩⟨i|)1 ⊗ (|µ⟩⟨ν|)2.

Hierarchy of entanglement detection criteria for random high-dimensional states The PT, ρT1 12, of ρ12 with respect to the subsystem 1, is defined as ρT1 12 = ∑ 1≤i,j≤d1 ∑ 1≤µ,ν≤d2 aµν ij (|j⟩⟨i|)1 ⊗ (|µ⟩⟨ν|)2

Reference 8

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Observation ab22e6d1-fa8e-439d-bc82-95764ca146df · outbound

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Reference 9

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Observation 8a56e8d6-b6a5-4a77-bb18-728ea3040f1c · outbound

This paper cites I1(2) denotes the d1(2)-dimensional identity matrix, whereas ρ1(2) = Tr2(1) ρ12 is the reduced density matrix correspond- ing to subsystem 1 (2).

Hierarchy of entanglement detection criteria for random high-dimensional states I1(2) denotes the d1(2)-dimensional identity matrix, whereas ρ1(2) = Tr2(1) ρ12 is the reduced density matrix correspond- ing to subsystem 1 (2)

Reference 10

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Observation 02e6c863-b166-4ab5-9360-6c9af3bd9162 · outbound

This paper cites The von Neumann en- tropy, S(σ) is defined as S(σ) = − Trσ log2 σ for a quantum state, σ [97–100].

Hierarchy of entanglement detection criteria for random high-dimensional states The von Neumann en- tropy, S(σ) is defined as S(σ) = − Trσ log2 σ for a quantum state, σ [97–100]

Reference 11

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Observation 7c15c7bd-4b25-42f9-8baf-0c6a72020a15 · outbound

This paper cites This leads to ρRl 12 1 ≤ d1 s d1d2 + k d1d2k + 1 = q fRl (k, d1, d2), ( 8) with fRl (k, d1, d2) = d2 1 d1d2+k d1d2k+1 > 0, ∀ k ∈ (2, d1d2).

Hierarchy of entanglement detection criteria for random high-dimensional states This leads to ρRl 12 1 ≤ d1 s d1d2 + k d1d2k + 1 = q fRl (k, d1, d2), ( 8) with fRl (k, d1, d2) = d2 1 d1d2+k d1d2k+1 > 0, ∀ k ∈ (2, d1d2)

Reference 12

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Observation 36334465-4b76-4393-ba24-e8cf42242c9f · outbound

This paper cites Let {gi} min[d2 1,d2 2] i=1 be the set of singular values of G.

Hierarchy of entanglement detection criteria for random high-dimensional states Let {gi} min[d2 1,d2 2] i=1 be the set of singular values of G

Reference 13

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Observation f2066d86-3555-41c8-8787-dd96404a64c1 · outbound

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Reference 14

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Observation 12b86434-80a0-47b2-84d4-ee39d3253ca5 · outbound

This paper cites Ollivier and W.

Hierarchy of entanglement detection criteria for random high-dimensional states Ollivier and W

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Observation 1e38111b-2c13-48bb-a1c7-7cd71038cdc2 · outbound

This paper cites An introduction to quantum discord and non-classical correlations beyond entanglement.

Hierarchy of entanglement detection criteria for random high-dimensional states An introduction to quantum discord and non-classical correlations beyond entanglement

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Observation 1a252916-8eda-4f35-acbb-3bfbcc51a9aa · outbound

This paper cites Brunner, D.

Hierarchy of entanglement detection criteria for random high-dimensional states Brunner, D

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Observation 2b43bd1d-65cd-4b60-a32e-442d57912521 · outbound

This paper cites Horodecki, P.

Hierarchy of entanglement detection criteria for random high-dimensional states Horodecki, P

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Observation f36052d3-76c7-4971-aaaa-d26000e578a6 · outbound

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Hierarchy of entanglement detection criteria for random high-dimensional states Pirandola, J

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Observation 256a518b-47d4-40da-af07-cfafe53e986d · outbound

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Hierarchy of entanglement detection criteria for random high-dimensional states Gisin, G

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Observation 5395cf84-3960-4c86-9b37-6d78d2f98f12 · outbound

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Hierarchy of entanglement detection criteria for random high-dimensional states Scarani, H

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Observation 15d773b7-e6f5-484b-a2d4-c8fd68366725 · outbound

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Hierarchy of entanglement detection criteria for random high-dimensional states Raussendorf and H

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Observation 80fd09f3-65f3-4ac0-bfe3-7862a1b26052 · outbound

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Hierarchy of entanglement detection criteria for random high-dimensional states Babazadeh, M

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Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

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Hierarchy of entanglement detection criteria for random high-dimensional states Yu and N.-l

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Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

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Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.485941Z

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Unavailable: canonical work link unavailable.

Observation a318df74-61c8-4660-83f2-22ac0ca87b6f · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.489153Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41eaaec5-f0a5-4554-a43b-c4896949f87a · outbound

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

Hierarchy of entanglement detection criteria for random high-dimensional states Peres, Separability criterion for density matrices, Phys

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.492741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d56daf8-5670-4e6d-8b51-c437766aee91 · outbound

This paper cites Horodecki, P.

Hierarchy of entanglement detection criteria for random high-dimensional states Horodecki, P

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.496266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba7e11f0-52d0-4bbd-b23b-7b02c3d56186 · outbound

This paper cites Horodecki and M.

Hierarchy of entanglement detection criteria for random high-dimensional states Horodecki and M

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.499796Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 876397a7-05b0-4d20-a1d5-8b33124167ab · outbound

This paper cites Horodecki and P.

Hierarchy of entanglement detection criteria for random high-dimensional states Horodecki and P

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.503737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cc1331f5-a8dd-4443-90ae-2d5aa302c60e · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.506794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bd36fdd-7c70-4f1e-ae50-c24856b1aeaa · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.510235Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea15de45-3c8f-4b74-bd33-e8445ea6cc90 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.513961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6911ec3-a1d3-4a18-8016-f45dbf1524e4 · outbound

This paper cites Chen and L.-A.

Hierarchy of entanglement detection criteria for random high-dimensional states Chen and L.-A

Reference 72

Resolution: verified exact; raw_fallback, observed 2026-08-06T12:27:33.024387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 61999016-e1dd-4d8f-a38c-3d598f3d34f7 · outbound

This paper cites Rudolph, A separability criterion for density operators, Journal of Physics A: Mathematical and General 33, 3951 (2000).

Hierarchy of entanglement detection criteria for random high-dimensional states Rudolph, A separability criterion for density operators, Journal of Physics A: Mathematical and General 33, 3951 (2000)

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.520545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8223b28-dcff-4ffb-90e2-3c2666daa564 · outbound

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

Hierarchy of entanglement detection criteria for random high-dimensional states Rudolph, Some properties of the computable cross- norm criterion for separability, Phys

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.523853Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2bc295b0-a608-4ec6-9cca-ac30c322f405 · outbound

This paper cites Rudolph, Further results on the cross norm criterion for separability, Quantum Information Processing 4, 219 (2005).

Hierarchy of entanglement detection criteria for random high-dimensional states Rudolph, Further results on the cross norm criterion for separability, Quantum Information Processing 4, 219 (2005)

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.528255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 63a6ce78-7970-4e69-87f3-fd246d86ea33 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.531674Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c9798ad-ef63-4f0e-9b4a-5c7649fcf73b · outbound

This paper cites Gühne, P.

Hierarchy of entanglement detection criteria for random high-dimensional states Gühne, P

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-06T12:27:32.535130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee0f80ff-2979-4db1-a010-2c0532eebe44 · outbound

This paper cites Chru´ sci ´ nski and G.

Hierarchy of entanglement detection criteria for random high-dimensional states Chru´ sci ´ nski and G

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.787791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2b3e0be2-c903-4cbd-9fcb-dccfb5ecd534 · outbound

This paper cites Gühne, P.

Hierarchy of entanglement detection criteria for random high-dimensional states Gühne, P

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.777758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f35b58a4-e559-46e1-964e-80c551c052a9 · outbound

This paper cites Gittsovich, O.

Hierarchy of entanglement detection criteria for random high-dimensional states Gittsovich, O

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.767155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 89cf935a-3916-4209-9d25-4e551fc1f0aa · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 81

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.757242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4999d5f3-5874-4a68-9025-4286fe893da0 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 82

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.746710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9a3399e4-ebab-4398-bf95-f9753880e09a · outbound

This paper cites Hulpke and D.

Hierarchy of entanglement detection criteria for random high-dimensional states Hulpke and D

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.736320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 79fa34fa-9b59-48d5-b718-988f6082e144 · outbound

This paper cites Vidal and R.

Hierarchy of entanglement detection criteria for random high-dimensional states Vidal and R

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.726628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 43c1aa2c-a810-426d-8325-5ce3c2445f05 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 85

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.717311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0a5024c2-cc70-4bb9-b361-f85028090c7a · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 86

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.707176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e5c48fbc-51f6-4a88-adb6-a6bf14af5422 · outbound

This paper cites Bengtsson and K.

Hierarchy of entanglement detection criteria for random high-dimensional states Bengtsson and K

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.697994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 22c2a8ae-4c5e-44a5-b847-2c3d09f4c580 · outbound

This paper cites Hayden, D.

Hierarchy of entanglement detection criteria for random high-dimensional states Hayden, D

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.686501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9ab3af7a-b47b-41bf-ab77-97276479a7df · outbound

This paper cites Enriquez, F.

Hierarchy of entanglement detection criteria for random high-dimensional states Enriquez, F

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.675814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ccd4ef24-910c-43b3-9553-0888d86180e8 · outbound

This paper cites Kłobus, A.

Hierarchy of entanglement detection criteria for random high-dimensional states Kłobus, A

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.665470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2347e48b-1126-4a20-b206-4f7e3547a380 · outbound

This paper cites Gross, S.

Hierarchy of entanglement detection criteria for random high-dimensional states Gross, S

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.654768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e2c41e40-de21-4b8e-9e8a-cc85496013f4 · outbound

This paper cites Rethinasamy, S.

Hierarchy of entanglement detection criteria for random high-dimensional states Rethinasamy, S

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.644290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 63d8fec7-5efa-4689-8a05-215f1d4a653e · outbound

This paper cites Hastings, Superadditivity of communication capacity using entangled input, Nature Physics 5, 255 (2009).

Hierarchy of entanglement detection criteria for random high-dimensional states Hastings, Superadditivity of communication capacity using entangled input, Nature Physics 5, 255 (2009)

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.623834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 69374262-84d0-460a-84cb-6387ee85a260 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 95

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.613133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation af79c5bd-cc3c-4f7d-85d1-84fbd10b95c5 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 96

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.602112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ac702bab-c844-45ea-b5a6-91984d96903e · outbound

This paper cites Granade, C.

Hierarchy of entanglement detection criteria for random high-dimensional states Granade, C

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.592509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1e4f634b-49e3-4763-b716-72e3e7299b76 · outbound

This paper cites an unresolved cited work.

Hierarchy of entanglement detection criteria for random high-dimensional states Unresolved cited work

Reference 98

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:27:33.582228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9750b34a-9965-4ad2-9af6-7ab78da4f62b · outbound

This paper cites Žnidariˇ c, T.

Hierarchy of entanglement detection criteria for random high-dimensional states Žnidariˇ c, T

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.571487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 696cf4ff-ebd8-48ac-9766-2d5f563c71fe · outbound

This paper cites Hamma, S.

Hierarchy of entanglement detection criteria for random high-dimensional states Hamma, S

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.560526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f5188744-fef8-4b24-988a-7ac3d429bd4c · outbound

This paper cites Gupta, S.

Hierarchy of entanglement detection criteria for random high-dimensional states Gupta, S

Reference 101

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.549918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 081f4f2e-5e56-4db8-8993-6ae65c25fb21 · outbound

This paper cites Gupta, A.

Hierarchy of entanglement detection criteria for random high-dimensional states Gupta, A

Reference 102

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:27:33.539631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers