Paper Citation Record · LEDGER

Tensor Network Representations for Intrinsically Mixed-State Topological Orders

As of 10 August 2026, this Paper Citation Record lists 72 of 72 outbound references and 2 inbound Pith citation observations for arXiv:2507.22989.

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

pith.paper-citation-record.v1
2507.22989 v1

Coverage vector

measured 72 of 72 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T11:26:06.985091Z

measured 74 of 74 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T11:26:00.794772Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T13:41:25.776198Z

Reference resolution

72 of 72 outbound references displayed

verified exact1
verified fuzzy18
unresolved50
parse uncertain2
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External citation measurements

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Outbound references

Observation 57e8da51-c2a3-4d62-82a9-0b65b17154ac · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 1

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Observation 0ad3ccb3-66bf-45a4-bd2a-d36d20a20b36 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 2

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Observation c3c5b1c3-90a7-49e8-94e3-c838304fb84e · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 3

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Observation 4850d356-5799-4628-a384-d042bea00f47 · outbound

This paper cites Tensor Network Representations for Intrinsically Mixed-State Topological Orders.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Tensor Network Representations for Intrinsically Mixed-State Topological Orders

Reference 4

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Observation 3d9af397-5a47-4117-9b77-44c7c7e2f992 · outbound

This paper cites (30) 8 The single-link support of the Kraus operators makes the doubled space approach unnecessary.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders (30) 8 The single-link support of the Kraus operators makes the doubled space approach unnecessary

Reference 5

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Observation feab2063-594f-4393-9159-b46a960144f1 · outbound

This paper cites 6; they represent the most general form for the decoherence of an arbitrary individual anyonmaeb in the ZN topological phase.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders 6; they represent the most general form for the decoherence of an arbitrary individual anyonmaeb in the ZN topological phase

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.508067Z

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Observation d799d768-44b8-40fd-9b29-e706e4266581 · outbound

This paper cites The local channel acts as: Nl [(·)] = 1 2 ((·) + XlZl−a(·)XlZl−a).

Tensor Network Representations for Intrinsically Mixed-State Topological Orders The local channel acts as: Nl [(·)] = 1 2 ((·) + XlZl−a(·)XlZl−a)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.491315Z

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Observation 7e95d007-921f-4be5-acee-baa2f04b6d87 · outbound

This paper cites (44) Since e2m2 is a self-boson, the bases ofHl and H∗ l can separately be taken to diagonalizeX 2 l and Z 2 l , which al- lows us to skip the doubled representation altogether.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders (44) Since e2m2 is a self-boson, the bases ofHl and H∗ l can separately be taken to diagonalizeX 2 l and Z 2 l , which al- lows us to skip the doubled representation altogether

Reference 8

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Observation c49aead5-65d1-4afd-91e9-7d54a4ae20e5 · outbound

This paper cites III: X 2 |x, z⟩ = ( −1)x |x, z⟩ , Z 2 |x, z⟩ = (−1)z |x, z⟩.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders III: X 2 |x, z⟩ = ( −1)x |x, z⟩ , Z 2 |x, z⟩ = (−1)z |x, z⟩

Reference 9

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Observation 1d9e6860-41a8-42c8-80bf-f9abc0e68a5e · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 10

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Observation 2db82a80-4605-4253-8c94-91c7dc25370c · outbound

This paper cites Freedman, A.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Freedman, A

Reference 11

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Observation a0ae7614-794b-4ca1-a3bd-d3df338dee89 · outbound

This paper cites Moessner and J.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Moessner and J

Reference 12

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Observation 22dc20cf-bb85-4a9e-bcfa-e9e6130c7745 · outbound

This paper cites McGinley and N.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders McGinley and N

Reference 13

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Observation ee1afd1c-c5bd-479d-86e7-8ff9fd6d5ff0 · outbound

This paper cites de Groot, A.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders de Groot, A

Reference 14

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Observation 4533118f-2459-4b68-b2ad-8f02218dc753 · outbound

This paper cites Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic

Reference 15

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Observation 6dd9d12a-81fe-4886-9ff8-b93ae6f17f43 · outbound

This paper cites Ma and C.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Ma and C

Reference 16

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Observation ee5c7401-05d0-429c-aa09-4c498ce8681c · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 17

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Observation d1eb9d90-0a02-4482-a88c-6ea74a1c577e · outbound

This paper cites Zhang, K.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Zhang, K

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.350376Z

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Observation da2630e9-a784-42d4-8b8a-08808583fba1 · outbound

This paper cites Ma and A.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Ma and A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.334739Z

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Observation 73839fb1-5bfd-408f-912f-e2eac251a3dc · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 20

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Observation bcae7c72-5084-4371-b1e9-eff697409fb3 · outbound

This paper cites Guo and S.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Guo and S

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:02.755791Z

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Observation fcf5c4e7-15a0-435b-a535-a5a53fdb73ff · outbound

This paper cites Guo, J.-H.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Guo, J.-H

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.308014Z

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Observation ad5fa622-af79-475f-b0af-d5387182733c · outbound

This paper cites Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions

Reference 23

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 24

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 25

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Observation f874d45c-7b78-4df8-a1db-0f52ee362ea6 · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 26

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Observation b5fb3979-0e06-4f45-bcd2-aa0f21421806 · outbound

This paper cites Sohal and A.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Sohal and A

Reference 27

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Observation f37bd66f-fb01-4b77-bd3d-7db7ec6a1df8 · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 28

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Observation 98a321f5-0764-4276-ad8d-0e49fcabbf48 · outbound

This paper cites Replica topological order in quantum mixed states and quantum error correction.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Replica topological order in quantum mixed states and quantum error correction

Reference 29

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Observation b8a39dee-b424-4315-b9d7-92f51d6b6cc3 · outbound

This paper cites Chen and T.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Chen and T

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.242991Z

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Observation 2b964a37-0575-4308-81eb-ce2b20902522 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 31

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Observation 01ca7fe2-216c-4981-aa17-b9d40ba66e4d · outbound

This paper cites Mixed-state TQFTs.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Mixed-state TQFTs

Reference 32

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Observation f5c3660f-0429-4edb-a21e-c916fa0d04fd · outbound

This paper cites Zhang, Y.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Zhang, Y

Reference 33

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Observation bbaf5498-e98f-4d57-96c9-a9ebbe8da581 · outbound

This paper cites Wang, X.-D.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Wang, X.-D

Reference 34

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Observation ce7e3632-4e28-445b-8405-7d785e2727f1 · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 35

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Observation 3aa24228-7643-4203-95b2-16ba62e9d2c3 · outbound

This paper cites Sang and T.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Sang and T

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:04.060439Z

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Observation ad26d08b-472e-470d-aec6-b7989879d436 · outbound

This paper cites Higher-form anomaly and long-range entanglement of mixed states.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Higher-form anomaly and long-range entanglement of mixed states

Reference 37

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Observation 2145b2d9-ce35-44d5-958e-c2c06cb534fd · outbound

This paper cites How Much Entanglement Is Needed for Topological Codes and Mixed States with Anomalous Symmetry?.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders How Much Entanglement Is Needed for Topological Codes and Mixed States with Anomalous Symmetry?

Reference 38

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Observation 5b292eb7-ca71-44b8-b111-39ca1ec4f8e9 · outbound

This paper cites Kikuchi, K.-S.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Kikuchi, K.-S

Reference 39

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Observation ae8e9838-f4aa-4239-9a28-e082acba5681 · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 40

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Observation 44634063-b185-4809-a83b-96f53cb88f25 · outbound

This paper cites Bombin, Topological subsystem codes, Phys.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Bombin, Topological subsystem codes, Phys

Reference 41

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Observation f0968e7b-476f-4d2c-8006-40ee68c64add · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 42

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Observation c58833af-2868-45e2-ad5d-22d38097af21 · outbound

This paper cites Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics321, 2–111 (2006).

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics321, 2–111 (2006)

Reference 43

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Observation a61cedce-b61b-4b95-93ca-088e356121b5 · outbound

This paper cites Kapustin and L.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Kapustin and L

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.126177Z

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Observation 45cf0864-75f4-4f34-8ced-ef07dfee3f5e · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:08.110251Z

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Observation 2f90bbb8-bbef-4d0e-8480-ba3ecdbfed2f · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 46

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Observation 21223096-bb98-4c3e-8450-da8a2185cd06 · outbound

This paper cites Buerschaper, M.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Buerschaper, M

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.094656Z

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Observation 05a5359a-a82d-41ca-ab10-41fe4c810196 · outbound

This paper cites Zhu and G.-M.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Zhu and G.-M

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:04.913494Z

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Observation 4ee78c31-4fb7-48a4-beac-3df0749e9ecb · outbound

This paper cites Buerschaper, J.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Buerschaper, J

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:08.068347Z

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Observation 29de073a-a7ba-4981-8775-c70e65ae45ce · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:08.051320Z

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Observation 06bfbe48-556e-498a-8b54-3c848fca7e52 · outbound

This paper cites Levin and C.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Levin and C

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:05.066790Z

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Observation 02555668-583d-4f3d-ac97-19a419b8ca52 · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:08.024912Z

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Observation dac00a2b-f948-4ce6-9bf2-c2916ec68c00 · outbound

This paper cites Gu and X.-G.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Gu and X.-G

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:05.250918Z

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Observation 4be06cdc-adc0-4def-bfd6-516e4bd28adf · outbound

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Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:07.997488Z

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Observation ad3077b3-90a1-491b-939a-aaace921112b · outbound

This paper cites Duivenvoorden, M.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Duivenvoorden, M

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:07.981947Z

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Observation 2b02d77a-ee90-4319-a157-8c538aa840cb · outbound

This paper cites Zhang, W.-T.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Zhang, W.-T

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:07.967150Z

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Observation d5f559ab-a479-49b7-b7e7-d13cc22d4902 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:07.951175Z

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Observation b081cd3b-aa10-4b8f-856f-1cbf348ef7d2 · outbound

This paper cites Zhu, J.-Y.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Zhu, J.-Y

Reference 58

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Observation 16c96d7c-3a02-4060-9783-b062de717a9b · outbound

This paper cites Tensor network formulation of symmetry protected topological phases in mixed states.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Tensor network formulation of symmetry protected topological phases in mixed states

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:05.662699Z

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Observation aa4c22b9-ff5e-4ddb-ad35-bfef16a50a66 · outbound

This paper cites Iqbal, K.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Iqbal, K

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:26:07.925048Z

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Observation 741cc44b-8fad-4fb2-b5be-3bab1abe496e · outbound

This paper cites Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics303, 2–30 (2003).

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics303, 2–30 (2003)

Reference 61

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:05.787542Z

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Observation f97eb044-e312-4bd7-a473-cd457b403c0a · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:05.813066Z

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Observation 43b147a8-c449-4ea9-b8d5-31f9802d1611 · outbound

This paper cites Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications 10, 285 (1975).

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Choi, Completely positive linear maps on complex matrices, Linear Algebra and its Applications 10, 285 (1975)

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:05.892782Z

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Observation 07aa1f59-5829-4bb2-9e19-727966457be6 · outbound

This paper cites Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Reports on Mathematical Physics3, 275 (1972).

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Reports on Mathematical Physics3, 275 (1972)

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.037805Z

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Observation 063e7201-98ca-492a-863f-7addc73205d9 · outbound

This paper cites A Universal Circuit Set Using the $S_3$ Quantum Double.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders A Universal Circuit Set Using the $S_3$ Quantum Double

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.152651Z

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Observation 576a49ba-beeb-4b54-b9b8-6dca7f43fe0a · outbound

This paper cites Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.253807Z

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Observation 0fa4fb99-bdf6-46dc-bbad-3e280844abbe · outbound

This paper cites Beigi, P.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Beigi, P

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.366568Z

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Observation 788bb2bb-3768-4141-83ba-c7d000a15e84 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 68

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:07.856000Z

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Observation d8892576-dc8b-43a6-9f55-012b4470e3b4 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.621909Z

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Observation 08989b62-5d49-483e-96fb-2632c5c253ad · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.764950Z

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Observation b444b520-5f19-43be-952b-8cd3fe459572 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-06T11:26:06.907975Z

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Observation 2bb62bf4-eb55-4f1b-bd45-218f13392dc9 · outbound

This paper cites an unresolved cited work.

Tensor Network Representations for Intrinsically Mixed-State Topological Orders Unresolved cited work

Reference 72

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:26:07.829144Z

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Pith citing papers

Observation 4850d356-5799-4628-a384-d042bea00f47 · inbound