Paper Citation Record · LEDGER

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator

As of 8 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2606.29487.

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pith.paper-citation-record.v1
2606.29487 v1

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measured 39 of 39 reference resolution

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39 of 39 outbound references displayed

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Outbound references

Observation c77c66a0-22a9-484f-aa57-2aa7f40e58df · outbound

This paper cites Then 1−Pr[A ε]≤2 exp − ε2d 4 .(12) Proof.By Lemma II.3, the set A′+B′ 2 is contained in the sphere of radius1− ε2 8.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Then 1−Pr[A ε]≤2 exp − ε2d 4 .(12) Proof.By Lemma II.3, the set A′+B′ 2 is contained in the sphere of radius1− ε2 8

Reference 1

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Observation 1db2db4f-6c33-4525-b16e-3ec62fe18cb6 · outbound

This paper cites By Theorem II.4, Pr[|f−m f |> ε]≤4 exp − ε2d 4 ,(17) which has the asserted form after renaming the universal con- stants.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator By Theorem II.4, Pr[|f−m f |> ε]≤4 exp − ε2d 4 ,(17) which has the asserted form after renaming the universal con- stants

Reference 2

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Observation 72becbc8-d961-4e06-96b5-eaca64de77ce · outbound

This paper cites Then 1−Pr[A ε]≤2 exp − ε2(d−1) 4 .(25) Proof.By above state (or Lemma II.3), the set A′+B′ 2 is con- tained in the hyperdisk of radius1− ε2 8.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Then 1−Pr[A ε]≤2 exp − ε2(d−1) 4 .(25) Proof.By above state (or Lemma II.3), the set A′+B′ 2 is con- tained in the hyperdisk of radius1− ε2 8

Reference 3

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Observation 3cac465f-a806-4433-97ff-0b74991e3a2d · outbound

This paper cites By Proposition III.1, Pr[|f(x)−m f | ≥ε]≤4 exp −(d−1)ε 2 4κ2 ,(28) which has the asserted form after renaming the universal con- stants.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator By Proposition III.1, Pr[|f(x)−m f | ≥ε]≤4 exp −(d−1)ε 2 4κ2 ,(28) which has the asserted form after renaming the universal con- stants

Reference 4

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Observation 99cef1bc-3943-42b8-960b-d609140b0254 · outbound

This paper cites an unresolved cited work.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Unresolved cited work

Reference 5

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Observation 50fe7d65-d69c-4da7-b6f9-ebfd863c8c4c · outbound

This paper cites Boucheron, G.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Boucheron, G

Reference 6

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Observation 2358301f-f976-4722-bb46-5a631a90a922 · outbound

This paper cites A topological application of the isoperimetric inequality,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator A topological application of the isoperimetric inequality,

Reference 7

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Observation 0870f19d-e677-4413-bd18-335dd5b66952 · outbound

This paper cites L ´evy,Probl `emes concrets d’analyse fonctionnelle, Gauthier- Villars, Paris (1951).

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator L ´evy,Probl `emes concrets d’analyse fonctionnelle, Gauthier- Villars, Paris (1951)

Reference 8

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Observation 8448fc0d-3556-4e4d-9b0b-1505c7df49af · outbound

This paper cites Ledoux,The Concentration of Measure Phenomenon, AMS Mathematical Surveys and Monographs,89, American Mathe- matical Society (2001).

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Ledoux,The Concentration of Measure Phenomenon, AMS Mathematical Surveys and Monographs,89, American Mathe- matical Society (2001)

Reference 9

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Observation 74b3e0a1-689c-445e-986f-debeab3dcd86 · outbound

This paper cites A new proof of the theorem of A. Dvoret- zky’s on cross-sections of convex bodies,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator A new proof of the theorem of A. Dvoret- zky’s on cross-sections of convex bodies,

Reference 10

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Observation fee81db9-fd5a-4615-a496-e58eb2f2c943 · outbound

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Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Unresolved cited work

Reference 11

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Observation 1ca0f797-5c78-4924-90f9-242376848531 · outbound

This paper cites Concentration of measure and isoperimetric in- equalities in product spaces,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Concentration of measure and isoperimetric in- equalities in product spaces,

Reference 12

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Observation c0a17d4a-9cfe-48e9-9b1a-a15a1381910a · outbound

This paper cites A New Look at Independence,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator A New Look at Independence,

Reference 13

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Observation d34bdf5c-cb91-4a8b-9d20-69e2549474e7 · outbound

This paper cites Vershynin,High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge University Press (2018).

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Vershynin,High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge University Press (2018)

Reference 14

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Observation 9d927a74-331d-4d9e-859e-e9727d00b5fa · outbound

This paper cites The dimension of almost spherical sections of convex bodies,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator The dimension of almost spherical sections of convex bodies,

Reference 15

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Observation a4cd9bf9-0c95-436a-bcf8-83d9c9aeb519 · outbound

This paper cites The Concentration Phenomenon and Linear Structure of Finite-Dimensional Normed Spaces,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator The Concentration Phenomenon and Linear Structure of Finite-Dimensional Normed Spaces,

Reference 16

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Observation 58b644f4-2fea-45c2-8189-3141cdb3064b · outbound

This paper cites The heritage of P. L´evy in geometric functional analysis,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator The heritage of P. L´evy in geometric functional analysis,

Reference 17

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Observation dcb2c11b-022a-4646-beff-e4a06f441969 · outbound

This paper cites Constructions de suites sym ´etriques,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Constructions de suites sym ´etriques,

Reference 18

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Observation 48d5793f-5e73-4e79-9101-fc543c24646d · outbound

This paper cites Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups,

Reference 19

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Observation 8aebbfbb-f9ef-4649-bc86-51d5db953bec · outbound

This paper cites Lo- cal Random Quantum Circuits are Approximate Polynomial- Designs,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Lo- cal Random Quantum Circuits are Approximate Polynomial- Designs,

Reference 20

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Observation 6f7e078f-f70b-4e60-9a30-c2d847b44e5e · outbound

This paper cites Canonical typicality,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Canonical typicality,

Reference 21

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Observation 77159a43-f655-44fa-801d-0f1e6adc7c73 · outbound

This paper cites Random quantum circuits are approximate 2-designs,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Random quantum circuits are approximate 2-designs,

Reference 22

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Observation 9fff443d-b88a-4d94-9851-9d206825af79 · outbound

This paper cites Randomiz- ing quantum states: Constructions and applications,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Randomiz- ing quantum states: Constructions and applications,

Reference 23

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Observation d81471c2-8238-41ac-9763-0b047588fb4f · outbound

This paper cites Aspects of generic entanglement,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Aspects of generic entanglement,

Reference 24

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Observation fcb47e7f-737f-4a41-8a31-54253d791f8f · outbound

This paper cites Large deviation bounds fork-designs,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Large deviation bounds fork-designs,

Reference 25

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Observation 697cd1c1-b500-4524-a051-732427ae64d1 · outbound

This paper cites Entanglement and the foundations of statistical mechanics,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Entanglement and the foundations of statistical mechanics,

Reference 26

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Observation 506aabe9-f850-4a1c-87ec-1bb6b03134bb · outbound

This paper cites Sample-size-reduction of quantum states for the noisy linear problem,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Sample-size-reduction of quantum states for the noisy linear problem,

Reference 27

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Observation a86c6c87-4910-4af3-86f2-0f3a379a3246 · outbound

This paper cites Quantum statistical query learning.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Quantum statistical query learning

Reference 28

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Observation d7964025-ed21-455f-b18a-179db16f3a1b · outbound

This paper cites Learning unitaries with quantum statistical queries,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Learning unitaries with quantum statistical queries,

Reference 29

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Observation e45ba592-0330-46bf-87df-d0f5a992628a · outbound

This paper cites Most Quantum States Are Too Entangled To Be Useful As Computational Resources,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Most Quantum States Are Too Entangled To Be Useful As Computational Resources,

Reference 30

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Observation 9436bd62-7c1d-4804-8bff-5352bcd1b4a3 · outbound

This paper cites Barren plateaus in quantum neural network training landscapes,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Barren plateaus in quantum neural network training landscapes,

Reference 31

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Observation 1bee8447-beab-4125-8b49-7de1325f6a1c · outbound

This paper cites Learning Quantum Processes with Quantum Statistical Queries.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Learning Quantum Processes with Quantum Statistical Queries

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:34:21.575540Z

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Observation 0806361e-d822-43dd-9000-dcffb5e7a3da · outbound

This paper cites Generalizations of the spher- ical isoperimetric inequality to uniformly convex Banach spaces,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Generalizations of the spher- ical isoperimetric inequality to uniformly convex Banach spaces,

Reference 33

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Observation 3912218b-245f-44d7-bc09-1338917b94c2 · outbound

This paper cites Concentration of Mea- sure for Quantum States with a Fixed Expectation Value,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Concentration of Mea- sure for Quantum States with a Fixed Expectation Value,

Reference 34

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Observation 12056966-c30b-4509-b048-d6a7242a0fe1 · outbound

This paper cites Gromov,Metric Structures for Riemannian and Non- Riemannian Spaces, Birkh¨auser Boston (1999).

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Gromov,Metric Structures for Riemannian and Non- Riemannian Spaces, Birkh¨auser Boston (1999)

Reference 35

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Observation 71e68bd5-a650-4fa2-86a1-c8e3b5a361be · outbound

This paper cites Matou ˇsek,Lectures on Discrete Geometry, Graduate Texts in Mathematics, vol.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Matou ˇsek,Lectures on Discrete Geometry, Graduate Texts in Mathematics, vol

Reference 36

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Observation ab2aa329-a71f-4890-90a3-0ebdfde09dc3 · outbound

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Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Unresolved cited work

Reference 37

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Observation 34f7bea6-7c24-4751-84dc-813fb14a3f23 · outbound

This paper cites The Brun-Minkowski inequality,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator The Brun-Minkowski inequality,

Reference 38

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Observation a7558303-4269-46ab-9316-d3a616ce3ee8 · outbound

This paper cites Topological methods in variational problems and their application to the differential geometry of surfaces,.

Concentration of Measure Phenomena for Quantum States on a Higher Dimensional Equator Topological methods in variational problems and their application to the differential geometry of surfaces,

Reference 39

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