Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T01:10:23.967947Z
Paper Citation Record · LEDGER
As of 16 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 3 inbound Pith citation observations for arXiv:2505.02125.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T01:10:23.967947Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:52:52.228456Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-25T07:50:28.831913Z
57 of 57 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 8317e498-dcd3-48cf-b57e-dabef6930a8c · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Thus, as discussed in Sec
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a2f09d57-4298-4572-873e-086ae14ca129 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4b37d02-7923-4304-86a1-79b562aae7f1 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 396d7a9a-65d9-4e7f-86e1-efe49d0d502f · outbound
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8bb1681b-a03e-4244-bb63-3c2d06ad2c32 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0061a09b-a80c-4341-a5b8-de1b924acc64 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8bd7ccc5-d04d-4eea-9629-a12fa41047c1 · outbound
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation db6055aa-cb30-46fc-88ad-45b4e36deedd · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Bluvstein, S
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8c5ffca6-d515-4b75-9fcd-594fdfad228d · outbound
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cfb465c0-ba46-4026-ad26-77f1aea5923f · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018)
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 79da2d2e-c99c-4857-bfe4-7d1ef6098bd2 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Bu ˇca and T
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 95731d1c-7a57-4838-829b-35a1ef065cb5 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions de Groot, A
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation da929132-1363-44ff-a4d9-d4ad26a8d8c1 · outbound
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4ee5725c-d18f-4682-aeff-f248cfa98673 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
Reference 14
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0eb9839f-9172-4405-ba9a-8e5b01d40543 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Symmetry Protected Topological Phases of Mixed States in the Doubled Space
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39e09319-1749-4b5a-b759-0fd1cca0a861 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 516a3921-4d0f-461c-ae04-cb6e049402e9 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5fe33f51-088a-4cc2-a724-eb3c4fa6e811 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ca2a290a-de6d-414a-a9dd-64bb31f8a598 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e54accea-3229-40b2-afed-c78edb1c9335 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 547a9a35-81a2-480c-881b-1f7d02b05b20 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the R\'enyi-1 Correlator
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cd860556-91cf-4c67-a10f-2b4344cd9344 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ece46dd-f277-4f63-8744-b6b31dc66060 · outbound
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b041635f-8837-460e-b354-cce76a0c0249 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions System-environmental entanglement in critical spin systems under $ZZ$-decoherence and its relation to strong and weak symmetries
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc92dc72-08d0-4fac-9006-5500f13340f3 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 25
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4164d6f1-df22-4fad-9537-4de42e1315af · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation abba03c3-452f-49a6-bf0f-a5f0be568be2 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c9500144-a2b2-44dd-a855-fdc6487410bb · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 05c937ed-10bf-4a3b-b612-81df1dc3e8b7 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f7b72907-43ab-4905-a553-8b5da85b4a25 · outbound
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7b1cbd0b-8f7d-4cc4-89c7-5850a8090f98 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Sohal and A
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a8c12db7-3405-465f-8e55-e7acda08aecf · outbound
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ae0b3c04-1b45-45ef-a065-e545be1084c4 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 279e6526-101a-4017-93ca-df30feffb2ee · outbound
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation daf6e4c8-885b-48cc-a201-a0b900a91bf0 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Petz, Sufficiency of channels over von neumann algebras, The Quarterly Journal of Mathematics 39, 97 (1988)
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b58d10f6-c754-4dda-bc99-8a621bc37647 · outbound
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f839dd5e-e49b-4f42-bb87-a0387483f513 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 85228ac3-ef98-43fb-b624-f158cabdfbc2 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Hauschild and F
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5305f0ae-ecfc-484e-bbde-d8bbf37d28cd · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Tensor Network Python (TeNPy) version 1
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a8a08c91-abc8-4944-93c0-40a63744813b · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6e199050-3ef8-4656-b697-f4dd69547573 · outbound
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 64d68765-9373-4ebf-aa6f-7d2144091cd0 · outbound
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a2ab2eb7-0f50-4835-8923-da0e9183a442 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Choi, Completely positive linear maps on complex ma- trices, Lin
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fe93ceac-9b66-4b11-971f-406293d2046a · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0e6d41ad-8371-4471-8e31-081358f0a756 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Universal Properties of Critical Mixed States from Measurement and Feedback
Reference 45
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7a2fd220-4e3b-4b16-a2a1-fbd47e5eb9eb · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e1c1f2bd-c919-4bbe-a071-d16e730c72ee · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Raussendorf and H
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 826f84e9-02ac-4433-aa27-d98bd7e3443f · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b29ea184-0b5e-47d6-958e-d5036897d052 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a2cb1afb-1259-4400-80d6-2048bde80a7d · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 458379ad-ea08-42be-9ce4-da10d78c0ced · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 51
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b49ca052-97cd-4d84-9db3-ee51c23b76ca · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 187f232f-67c3-41a2-90e6-ffd0117c09e3 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Unresolved cited work
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 30ba0e21-57d5-484d-b80e-b76a08170f3e · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Lecture Notes on the Theory of Open Quantum Systems
Reference 54
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Unavailable: canonical work link unavailable.
Observation e0146948-983e-4978-b946-80c6af5727f1 · outbound
Reference 55
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Unavailable: canonical work link unavailable.
Observation 895df6f7-3c1f-4e62-9bf0-57d6e3806f0f · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Weinstein, Y
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e1d017e5-f817-4591-917c-91a9251ca042 · outbound
R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions Entanglement negativity at the critical point of measurement-driven transition
Reference 57
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9f2c3ba5-52ca-44f7-bdfe-d08b3166285b · inbound
R\'{e}nyi and Shannon mutual information in critical and decohered critical system R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions
Reference 35
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ecab2227-b7cf-4d29-b386-09c5d500d511 · inbound
Succession of Ising criticality and its threshold in critical quantum Ising model subject to symmetric decoherence R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7963df86-75ba-4061-835e-379d27734e33 · inbound
Krylov Complexity and Mixed-State Phase Transition R\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions
Reference 70
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.