Paper Citation Record · LEDGER

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength

As of 8 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 2 inbound Pith citation observations for arXiv:2509.09340.

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

pith.paper-citation-record.v1
2509.09340 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T19:27:53.807789Z

measured 51 of 51 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T00:43:52.750282Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T21:18:59.512970Z

Reference resolution

49 of 49 outbound references displayed

verified exact0
verified fuzzy0
unresolved49
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c1672a2d-55ec-4b92-adcc-3b67625a1870 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:50.495598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 291416f5-be41-4789-8883-8fbf8d397722 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:50.644264Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d987a7c5-b246-41d8-83d7-18b3b367e5be · outbound

This paper cites Ambainis, M.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Ambainis, M

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:50.751027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14d1562f-f264-4178-b4a8-6fc3e74b63a5 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:50.910590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac3fa605-a2fe-4434-9d8f-f3fed79f44ad · outbound

This paper cites Nayak and P.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Nayak and P

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.011018Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e601c02-ccbc-4007-9199-c0c13e5eb6e1 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.152558Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c162ba9-ccde-437e-bed0-83f1cc352ed7 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.268461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a5dd3b3-d02d-4d94-b205-dbc3020a84a2 · outbound

This paper cites Macchiavello and G.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Macchiavello and G

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.337226Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 953ae6ac-b166-4a9b-bdbf-2579947a1122 · outbound

This paper cites Bowen and S.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Bowen and S

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.395517Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08e22f94-2fef-4c90-94c4-886d77460bb5 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.445015Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2cecd5cb-7311-42ff-a88b-bb537a069264 · outbound

This paper cites Gregoratti and R.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Gregoratti and R

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.491374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2c65749-9799-4ae5-bc50-a87a12db45ad · outbound

This paper cites Gregoratti and R.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Gregoratti and R

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.524069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a82ea1e1-9072-4721-b7a4-ec46ebb9a46f · outbound

This paper cites Buscemi, G.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Buscemi, G

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.550645Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b88002c2-cc29-4a77-818f-a701d9721409 · outbound

This paper cites Karumanchi, S.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Karumanchi, S

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.623097Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 31ece1fc-2978-456c-8add-1a3945ecdbac · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.698919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db0761a0-da37-4fbf-b752-ab7cd98526c2 · outbound

This paper cites Harraz, S.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Harraz, S

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.737818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56d9f8b2-4de5-42ff-a2f0-9d1328b7f17c · outbound

This paper cites Harraz, J.-Y.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Harraz, J.-Y

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.807072Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b07c1d6f-c04e-46e4-90aa-0ebd591440ea · outbound

This paper cites Chiribella and H.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Chiribella and H

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.891479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dec6919b-5a52-477a-9ee5-935deb5fd576 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:51.946939Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab582100-1735-4bc4-8504-c4c0ac133dd8 · outbound

This paper cites Lai, J.-D.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Lai, J.-D

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.034520Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b6aa374-c3f4-4a83-ad72-0c22dbc24969 · outbound

This paper cites Saha and U.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Saha and U

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.086434Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98fc3950-ff1b-4688-9abc-55b8af4c123d · outbound

This paper cites Banaszek, A.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Banaszek, A

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.177450Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 50908e33-5492-4087-9b38-bf716e7884bc · outbound

This paper cites Pirandola, C.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Pirandola, C

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.228456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 163467a5-76e9-4070-9954-42bfd7c4bbc7 · outbound

This paper cites Rubino, L.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Rubino, L

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.300695Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dde04030-2573-45d3-b5ee-f6ddfc71d7da · outbound

This paper cites Wang and L.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Wang and L

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.369446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2445275b-52c9-4376-b854-056031076f74 · outbound

This paper cites Hayden and C.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Hayden and C

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.433340Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d368daf-10d0-407e-9c57-3d8ea21a8a6b · outbound

This paper cites On environment-assisted capacities of quantum channels.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength On environment-assisted capacities of quantum channels

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.492529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b09140b-8b73-45a5-9307-e6e8cb61946a · outbound

This paper cites Karumanchi, S.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Karumanchi, S

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.540854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0aceeb06-b04e-4032-b768-b44364c47d11 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.611596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 712c1b00-a19a-4eb2-ad2c-bb6bcacb64fe · outbound

This paper cites Watrous, Bipartite subspaces having no bases distin- guishable by local operations and classical communica- tion, Phys.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Watrous, Bipartite subspaces having no bases distin- guishable by local operations and classical communica- tion, Phys

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.666746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4f60b0b-7c52-4c4c-84a2-5fa5509f0912 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.714354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1783ad8e-e20d-4b6d-a623-b64b6e5340e7 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.805709Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28069067-2cfc-478a-beac-5237d0fe87ea · outbound

This paper cites Heinosaari and O.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Heinosaari and O

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.863352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53eaa5ec-327d-45a0-84e5-bd06d7840542 · outbound

This paper cites Chiribella, S.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Chiribella, S

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:52.951459Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e717828a-b853-441f-81a8-eec2670e8ee2 · outbound

This paper cites Holevo, The capacity of the quantum channel with general signal states, IEEE Transactions on Information Theory44,269–273(1998).

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Holevo, The capacity of the quantum channel with general signal states, IEEE Transactions on Information Theory44,269–273(1998)

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.002159Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d14d3cff-e1a9-4908-8dec-4041dc5f5d50 · outbound

This paper cites Schumacher and M.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Schumacher and M

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.057667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98763a80-089b-41b1-a7b3-d3fc0ad6dc6f · outbound

This paper cites Some upper and lower bounds on PSD-rank.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Some upper and lower bounds on PSD-rank

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.117148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82467814-1d03-441c-9eb7-9f9631838072 · outbound

This paper cites Gouveia, P.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Gouveia, P

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.165423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8bc6f241-3e1f-4e42-a11d-c2b209223d13 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.248571Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c141db9c-403f-431f-88dd-78c5d489973f · outbound

This paper cites Horodecki, P.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Horodecki, P

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.303048Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a1df731-70c5-47a6-95fe-b15b9cc972e3 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.361298Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae4f2f9d-4b7e-4f64-bc4b-1c7a13060520 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.409936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ac27c1f-6554-424c-b9d2-dd11d538540d · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.465714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 680c1f1e-1fe0-4bae-9802-9ea6c0a818d8 · outbound

This paper cites Fawzi, J.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Fawzi, J

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.542813Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 989a878d-8218-4ddb-925a-0ac351f46452 · outbound

This paper cites Dall’Arno, S.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Dall’Arno, S

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.629838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d661950-0fd2-49ae-b740-2c6218ed8377 · outbound

This paper cites She sends the quantum system reliably through a perfect seven-dimensional quantum channel to Bob.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength She sends the quantum system reliably through a perfect seven-dimensional quantum channel to Bob

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.663036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e5e04a7-25fd-4640-8ae6-83a0c701ffb6 · outbound

This paper cites an unresolved cited work.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.705356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b560afbf-45f5-402b-968d-c77a88f9be2f · outbound

This paper cites Addition- ally, after getting the click of the P5 (P6) projector, he uses a {p, 1−p} ({ p 3 , 1− p 3 }) local randomness to outputy 5 andy 6 respectively.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Addition- ally, after getting the click of the P5 (P6) projector, he uses a {p, 1−p} ({ p 3 , 1− p 3 }) local randomness to outputy 5 andy 6 respectively

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.770252Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d43c993-c01d-49ff-89bf-98fc90ef159f · outbound

This paper cites Note that, in either cases j∈ {d−1,d,· · ·,d(d−1)}.

Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength Note that, in either cases j∈ {d−1,d,· · ·,d(d−1)}

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-04T19:27:53.807789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation b620c4ba-03fe-4423-837d-915deb3508a7 · inbound

Lost and found charge in quantum batteries cites this paper.

Lost and found charge in quantum batteries Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-04T00:43:52.750282Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32dacf14-f705-4574-a344-6821e5dfb559 · inbound

Demultiplexing Generalized Information via Quantum Transmission Lines cites this paper.

Demultiplexing Generalized Information via Quantum Transmission Lines Minimal Help, Maximal Gain: Environmental Assistance Unlocks Encoding Strength

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-07-03T21:18:59.514301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.