Paper Citation Record · LEDGER

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery

As of 23 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2607.15537.

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

pith.paper-citation-record.v1
2607.15537 v1

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T23:18:50.608004Z

measured 51 of 51 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

51 of 51 outbound references displayed

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verified fuzzy0
unresolved50
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malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b208c776-3597-45bb-9cba-b7b5c0a667fa · outbound

This paper cites Logarithms and entropies are measured in bits unless stated otherwise.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Logarithms and entropies are measured in bits unless stated otherwise

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:44.625156Z

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Observation 22ec31bf-9074-4f8d-bfe9-34dfae1817ec · outbound

This paper cites For independent uniformly distributed ordered ℓ-subsets S= (S 1 <· · ·< Sℓ), T= (T 1 <· · ·< Tℓ), define Mn,ℓ = ℓX a=1 1{Sa=Ta}.(A4) Lemma 6(Exact collision identity).

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery For independent uniformly distributed ordered ℓ-subsets S= (S 1 <· · ·< Sℓ), T= (T 1 <· · ·< Tℓ), define Mn,ℓ = ℓX a=1 1{Sa=Ta}.(A4) Lemma 6(Exact collision identity)

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:44.729864Z

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Observation 5dd3ac37-23dd-4730-b708-13894cabec4c · outbound

This paper cites Under the planted lawP, the input wordX∈ {0,1} n is uniform,Sis a uniformly chosen orderedℓ-subset of [n], and Ya =X Sa.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Under the planted lawP, the input wordX∈ {0,1} n is uniform,Sis a uniformly chosen orderedℓ-subset of [n], and Ya =X Sa

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:44.809419Z

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Observation ecd443f1-69ac-4e81-9843-7e95640fc445 · outbound

This paper cites It is therefore necessary to distinguish the planted law uniformly from every product lawP X QY , whereP X is the fixed uniform input marginal.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery It is therefore necessary to distinguish the planted law uniformly from every product lawP X QY , whereP X is the fixed uniform input marginal

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:44.910830Z

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Observation 1cfc6313-5d2a-48ac-9c03-d481f81803da · outbound

This paper cites The k-qubit diary M is maximally entangled with R, while the remaining registerHis maximally mixed after its purifierEis traced out.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery The k-qubit diary M is maximally entangled with R, while the remaining registerHis maximally mixed after its purifierEis traced out

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:44.962806Z

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Observation 1e5948df-37dd-4940-8907-756774b880de · outbound

This paper cites Fix ε and δ as in (14).

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Fix ε and δ as in (14)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.032909Z

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Observation 51e5cf37-b25e-4b91-8579-bb363e8190e7 · outbound

This paper cites , IB, each of size m.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery , IB, each of size m

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.178993Z

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Observation b85d4acc-3cc5-4fb2-aa78-44d1dd7f5e8b · outbound

This paper cites Let σ2 = Var(Z), M= max j πj.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Let σ2 = Var(Z), M= max j πj

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.265975Z

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Observation 4b40102b-1159-446b-a24e-cfb2dbe94805 · outbound

This paper cites The ratio of consecutive masses is a product of two nonincreasing factors, so πa is log-concave.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery The ratio of consecutive masses is a product of two nonincreasing factors, so πa is log-concave

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.312708Z

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Observation f6fc30d1-e223-4e23-996b-f08177b86e07 · outbound

This paper cites Lemma 21(Deterministic lower bound and averaged upper bound).Assume that ℓ = o(n).

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Lemma 21(Deterministic lower bound and averaged upper bound).Assume that ℓ = o(n)

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.384652Z

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Observation 2767face-b9b3-44be-ac9d-29724b771cd0 · outbound

This paper cites For r = 0, one has Gm,0 = 1.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery For r = 0, one has Gm,0 = 1

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.488750Z

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Observation 5a1702d1-0b24-4e71-b465-0816d1fc3fa1 · outbound

This paper cites For each block, let Pb = p(m,Lb) ai a,i , V b =V m,Lb , and define V= BX b=1 Vb =X(L), V max = max 1≤b≤B Vb.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery For each block, let Pb = p(m,Lb) ai a,i , V b =V m,Lb , and define V= BX b=1 Vb =X(L), V max = max 1≤b≤B Vb

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.584129Z

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Observation c3fee3b0-099b-4571-bf91-ca5d687d9ed4 · outbound

This paper cites Suppose now that Λn,ℓ,B − → ∞.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Suppose now that Λn,ℓ,B − → ∞

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.659491Z

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Observation cb34035c-33ab-45f7-b493-937409cd1914 · outbound

This paper cites an unresolved cited work.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.733908Z

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Observation 6aa91b1f-e429-45be-bb25-1c2fd38c447a · outbound

This paper cites Average Entropy of a Subsystem.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Average Entropy of a Subsystem

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.825044Z

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Observation b02181b4-75a6-428c-abf2-3d74ec68ec6b · outbound

This paper cites Black holes as mirrors: quantum information in random subsystems.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Black holes as mirrors: quantum information in random subsystems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:45.919376Z

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Observation 523507ac-be64-4296-9d19-1ef67d4d2116 · outbound

This paper cites Fast Scramblers.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Fast Scramblers

Reference 17

Resolution: malformed identifier; no resolver link, observed 2026-08-01T23:18:46.005000Z

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Observation 898c284c-7b32-405f-9d08-bedb26189b22 · outbound

This paper cites Quantum Computation vs. Firewalls.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Quantum Computation vs. Firewalls

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.077197Z

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Observation fda63472-d4e8-47f1-addd-ca6a90510f6c · outbound

This paper cites Efficient decoding for the Hayden-Preskill protocol.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Efficient decoding for the Hayden-Preskill protocol

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.191773Z

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Observation 0b4fe8d9-1881-4629-8790-25a9f0d25b61 · outbound

This paper cites Hayden-Preskill decoding from noisy Hawking radiation.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Hayden-Preskill decoding from noisy Hawking radiation

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.295915Z

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Observation f9f21d9c-14ff-4a03-8894-cd2b5cf31bf5 · outbound

This paper cites Hayden-Preskill protocol and decoding Hawking radiation at finite temperature.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Hayden-Preskill protocol and decoding Hawking radiation at finite temperature

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.399112Z

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Observation b6289674-95db-4ae8-92ee-c04d1e48222e · outbound

This paper cites Chaos in quantum channels.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Chaos in quantum channels

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.524739Z

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Observation 4f3aeea6-f080-4a18-ada3-4c69e438e9e3 · outbound

This paper cites Disentangling Scrambling and Decoherence via Quantum Teleportation.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Disentangling Scrambling and Decoherence via Quantum Teleportation

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.604470Z

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Observation 3b46d529-0366-482f-b212-69afbf9480f4 · outbound

This paper cites Verified Quantum Information Scrambling.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Verified Quantum Information Scrambling

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.710256Z

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Observation 226a612b-defd-423d-96b5-b9c77f9291a9 · outbound

This paper cites Recovery algorithms for Clifford Hayden-Preskill problem.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Recovery algorithms for Clifford Hayden-Preskill problem

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.798021Z

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Observation 0cf4ac59-ff45-4e2b-a979-32bd4955f8ec · outbound

This paper cites Decoding general error correcting codes and the role of complementarity.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Decoding general error correcting codes and the role of complementarity

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:46.945131Z

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Observation fd1f8551-8618-46cb-892f-907aca6e3995 · outbound

This paper cites Hayden-Preskill Recovery in Hamiltonian Systems.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Hayden-Preskill Recovery in Hamiltonian Systems

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:47.191482Z

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Observation b3bea1e9-da27-422e-9283-2d16ef5b93a1 · outbound

This paper cites Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:47.389622Z

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Observation 1dfdd4d4-693b-407d-8f62-2a2107f547b6 · outbound

This paper cites Simulating Floquet scrambling circuits on trapped-ion quantum computers.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Simulating Floquet scrambling circuits on trapped-ion quantum computers

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:47.550108Z

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Observation 4a6dfd4e-89fd-4b3f-be9d-94e781c59981 · outbound

This paper cites Decoupling with unitary approximate two-designs.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Decoupling with unitary approximate two-designs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:47.635111Z

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Observation 3f5fa39d-c3d2-48ad-a38b-53fcbadd30eb · outbound

This paper cites Decoupling with random quantum circuits.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Decoupling with random quantum circuits

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:47.811027Z

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Observation d80a7d02-df28-40b1-bcab-0d6ec3ad5471 · outbound

This paper cites Joint State-Channel Decoupling and One-Shot Quantum Coding Theorem.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Joint State-Channel Decoupling and One-Shot Quantum Coding Theorem

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:47.933645Z

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Observation 9a38ec06-7eba-4272-a9f5-9b67991e0e02 · outbound

This paper cites One-shot decoupling.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery One-shot decoupling

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:48.115295Z

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Observation 9d3213cd-bd9a-482d-8c2d-01478a54c920 · outbound

This paper cites Data processing for the sandwiched R\'enyi divergence: a condition for equality.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Data processing for the sandwiched R\'enyi divergence: a condition for equality

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:48.322521Z

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Observation b80b1117-a03b-49ea-8617-5376b3ed0e52 · outbound

This paper cites Information Radius,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Information Radius,

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:48.453506Z

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Observation 633be1d8-6f9e-4763-a273-299ef56a9a02 · outbound

This paper cites Monotonicity of a relative R\'enyi entropy.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Monotonicity of a relative R\'enyi entropy

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:48.629261Z

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Observation 2228d370-c286-4b78-81d1-6ae75b8a8efb · outbound

This paper cites Sandwiched R\'enyi Divergence Satisfies Data Processing Inequality.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Sandwiched R\'enyi Divergence Satisfies Data Processing Inequality

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:48.740343Z

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Observation 48856730-63c5-465e-b0a2-931e6d3017f5 · outbound

This paper cites Hanson-Wright inequality and sub-gaussian concentration.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Hanson-Wright inequality and sub-gaussian concentration

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:48.914079Z

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Observation 29ae6b28-fc93-45f0-bff4-12f4698b3739 · outbound

This paper cites On Tail Probabilities for Martingales,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery On Tail Probabilities for Martingales,

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.033022Z

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Observation 2a12133f-7bc7-43ca-903b-9e6a7296a4af · outbound

This paper cites A Survey of Results for Deletion Channels and Related Synchronization Channels,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery A Survey of Results for Deletion Channels and Related Synchronization Channels,

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.123119Z

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Observation 3c9d7f81-a489-4a2d-b4c7-aef5da273469 · outbound

This paper cites An Overview of Capacity Results for Synchronization Channels,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery An Overview of Capacity Results for Synchronization Channels,

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.254958Z

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Observation 7c9a155b-3713-41a5-9b7d-38b3e6186685 · outbound

This paper cites Quantum Insertion-Deletion Channels.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Quantum Insertion-Deletion Channels

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.393666Z

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Observation 368028ed-2ec2-4438-8063-a8b12c32b7ae · outbound

This paper cites A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length,

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.525048Z

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Observation d3960ef4-2bc6-4b25-b912-22490d2a3d15 · outbound

This paper cites Permutation-Invariant Quantum Coding for Quantum Deletion Channels,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Permutation-Invariant Quantum Coding for Quantum Deletion Channels,

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.742697Z

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Observation 296557c3-649e-43bd-84e0-0b66e3ea4ed5 · outbound

This paper cites The Equivalence between Correctability of Deletions and Insertions of Sep- arable States in Quantum Codes,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery The Equivalence between Correctability of Deletions and Insertions of Sep- arable States in Quantum Codes,

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:49.891926Z

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Observation 2d365434-86fe-4679-9321-ce6617a7f257 · outbound

This paper cites Quantum Deletion Codes Derived From Quantum Reed-Solomon Codes.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Quantum Deletion Codes Derived From Quantum Reed-Solomon Codes

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:50.015389Z

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Observation d514121a-7bfb-4dee-a02a-780e5ef94d43 · outbound

This paper cites The Equivalence of Quantum Deletion and Insertion Errors on Permutation-Invariant Codes,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery The Equivalence of Quantum Deletion and Insertion Errors on Permutation-Invariant Codes,

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:50.184960Z

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Observation 38ea2ac1-518b-474c-bbaa-122bfa41c1f4 · outbound

This paper cites A Theory of Quantum Error Correction for Permutation-Invariant Codes,.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery A Theory of Quantum Error Correction for Permutation-Invariant Codes,

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:50.306847Z

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Observation 02f01b57-ea5d-47fc-994a-0a22ef8087ee · outbound

This paper cites A Decoding Algorithm for Composite Errors Consisting of Deletions and Insertions in Quantum Deletion-Correcting Codes Based on Quantum Reed-Solomon Codes.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery A Decoding Algorithm for Composite Errors Consisting of Deletions and Insertions in Quantum Deletion-Correcting Codes Based on Quantum Reed-Solomon Codes

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:50.375703Z

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Observation 74d85266-f3a6-4d89-8496-f11f97115661 · outbound

This paper cites Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:50.514541Z

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Observation 5f60082a-0e33-4fd7-b85e-58691ed0f5a9 · outbound

This paper cites The Random Subsequence Model and Uniform Codes for the Deletion Channel.

Microscopic Side Information Controls Ordered Hayden--Preskill Recovery The Random Subsequence Model and Uniform Codes for the Deletion Channel

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-01T23:18:50.608004Z

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Pith citing papers

No inbound Pith citation observations are available.