Paper Citation Record · LEDGER

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities

As of 9 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2507.17117.

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

pith.paper-citation-record.v1
2507.17117 v1

Coverage vector

measured 48 of 48 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-06T15:08:02.589427Z

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

48 of 48 outbound references displayed

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External citation measurements

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Outbound references

Observation 05abce1a-2e50-4ba0-b92d-35baad80385a · outbound

This paper cites Horodecki, P.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Horodecki, P

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:03.069090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation eef7af5a-1138-4338-a43e-6b99e169c81d · outbound

This paper cites Vedral, Quantum entanglemen.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Vedral, Quantum entanglemen

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:03.060590Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6d6a47ff-82d7-4927-929d-930568c00318 · outbound

This paper cites Barrett, Nonsequential positive-operator-valued mea- surements on entangled mixed states do not always vio- late a Bell inequality.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Barrett, Nonsequential positive-operator-valued mea- surements on entangled mixed states do not always vio- late a Bell inequality

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:03.052805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ccf79e49-0df1-4592-83f3-fcd81bd55f46 · outbound

This paper cites Gisin, R.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Gisin, R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:03.044225Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4d5d3465-61cf-491c-86dc-15adf9d5c09c · outbound

This paper cites Bose, Quantum communication through an unmodu- lated spin chain.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Bose, Quantum communication through an unmodu- lated spin chain

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:03.036130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ed9bfa99-6511-4dde-b7b0-b654708c915c · outbound

This paper cites Gisin, G.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Gisin, G

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:03.028377Z

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Observation 23879067-14cf-4609-8445-4d9676b30dbd · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:03.020329Z

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Observation 0376f8eb-0b53-4467-a4c3-09863ebd0f08 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:03.012824Z

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Observation 4990b795-7c1e-4464-bbb7-e88d42cbc3ef · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:03.004455Z

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Observation 1c8b6f65-5402-48cb-926d-ff51e5163885 · outbound

This paper cites Horodecki, Entanglement measures.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Horodecki, Entanglement measures

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.995673Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cd07b62b-f161-4e9f-99ee-cc96fe396e76 · outbound

This paper cites G¨ uhne, M.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities G¨ uhne, M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.987321Z

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Observation e5cdb85f-28bc-4d3d-bbe8-d5940bb67d6d · outbound

This paper cites Szalay, Multipartite entanglement measures.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Szalay, Multipartite entanglement measures

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.978699Z

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Observation 7d40f935-77b1-4277-8f05-360385eaae61 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.970741Z

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Observation b75a1837-e864-4363-bcc3-2c325d5552ed · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.962173Z

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Observation 1f53eb81-9259-45f3-85f7-e50e9758f86a · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.952605Z

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Observation be79a004-72c5-4051-a2d3-8a56647da165 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.943460Z

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Observation aecee84d-c77d-400e-94b7-4c212a79efa9 · outbound

This paper cites Henderson, V.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Henderson, V

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.934680Z

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Observation 05bf3964-0a3f-48ad-b523-402837670a09 · outbound

This paper cites Moitra, R.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Moitra, R

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.926247Z

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Observation 144b99f6-ea7d-441f-a1b6-b0a2cf6a98f9 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.918220Z

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Observation 56feedd9-4cc2-4a6d-8950-d5fd23ba4d05 · outbound

This paper cites Schatzki, G.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Schatzki, G

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.909592Z

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Observation e99a35e8-7201-4ca9-a935-e64afdba8e73 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.901711Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 951ed84b-0478-4a22-9c1a-7ae4d889eda4 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.893059Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c14d1412-8f1e-46f7-9aa4-a993eac0304c · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.884384Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bb9e673e-1063-4d45-839f-3a1b8b3d8313 · outbound

This paper cites Zhou, Z.X.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Zhou, Z.X

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.875592Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 59da75b3-9539-42a9-8629-205f9951c35a · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.866194Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d0c940c0-72a9-4fb8-a424-53dd5084486f · outbound

This paper cites Foulds, V.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Foulds, V

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.857403Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d264fba0-3826-4be1-8f87-cd043b4d3a2e · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.849697Z

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Observation fe25d846-0a5f-4f95-ad52-ca6dd8ddf98d · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.840907Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 775547d4-2b23-4a5b-aa32-f480ffbacc0d · outbound

This paper cites Johri, D.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Johri, D

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.832767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9f07d900-1fac-404c-b808-aca39b0f5673 · outbound

This paper cites Suba¸ sı, L.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Suba¸ sı, L

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.825291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6de59811-ba5a-41c7-82ba-07e9cdb8be9f · outbound

This paper cites Yirka, Y.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Yirka, Y

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.816637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5278ee0f-2bb3-4f07-bf8b-c29397a00e21 · outbound

This paper cites Resource-efficient algorithm for estimating the trace of quantum state powers.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Resource-efficient algorithm for estimating the trace of quantum state powers

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:08:02.633109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d13f04b6-e70f-489b-9638-b865c1804fb4 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.807788Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d2e09a31-9d2d-4498-a253-5e2dd31f436f · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.799152Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d7d5122b-a011-4753-a4a5-f97b083f4c66 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.789967Z

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Observation 77ec3f59-2f82-4d49-b710-b7bfce1a6bb4 · outbound

This paper cites Neven, J.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Neven, J

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.781080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0c14b2f4-a1a7-43d5-8962-1e1c6dd11fac · outbound

This paper cites Natalini, P.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Natalini, P

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.773338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 84638283-c3a7-4016-b943-f6f89be496ee · outbound

This paper cites Hoeffding, Probability inequalities for sums of bounded random variables.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Hoeffding, Probability inequalities for sums of bounded random variables

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.763767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f22ed469-8262-4a1d-ac32-e573772ec201 · outbound

This paper cites Rotter, Dynamics of quantum systems.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Rotter, Dynamics of quantum systems

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.752972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e0d01e41-1ed5-4497-9666-e5a39694b436 · outbound

This paper cites Lloyd, M.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Lloyd, M

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.743288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2100603a-52d3-457a-bfa5-65e9d6761c27 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.732430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 83cd0bee-5bdf-49a6-b2ad-03b05063729e · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.723076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3948a6f2-a809-4d79-9ac9-f899b46ccafd · outbound

This paper cites Consiglio, J.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Consiglio, J

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.713033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 54423370-c5eb-4a1a-a920-672c2153b4f6 · outbound

This paper cites San Kim, Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities San Kim, Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.700538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6ba80902-1b83-4b46-b340-1ba63b4f2968 · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.687707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1a3259bf-0a5c-4143-a63c-18cfdcc5986b · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.676400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 656ccc29-6d03-4be0-8916-17db5db5e64c · outbound

This paper cites an unresolved cited work.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:08:02.659552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2d1e759a-7525-45a3-8acc-6aebafb1f410 · outbound

This paper cites cz 1,··· ,s is even.

Explicit Formulas for Estimating Trace of Reduced Density Matrix Powers via Single-Circuit Measurement Probabilities cz 1,··· ,s is even

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:08:02.645731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

No inbound Pith citation observations are available.