Pith Number

pith:TJ5YINI5

pith:2024:TJ5YINI5KIIFALFHQKSMWXDAP4

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Lower bounds on bipartite entanglement in noisy graph states

Aqil Sajjad, Don Towsley, Eneet Kaur, Kenneth Goodenough, Saikat Guha

Certain graph states keep strictly positive coherent information under any non-maximal depolarizing noise in the pre-edge model.

arxiv:2404.09014 v2 · 2024-04-13 · quant-ph

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Claims

C1strongest claim

We find a family of graph states that maintain a strictly positive coherent information for any amount of (non-maximal) depolarizing noise.

C2weakest assumption

The specific noise model in which depolarizing noise acts independently on each initial qubit before the CZ operations that create the graph edges (as stated in the abstract's description of the model considered).

C3one line summary

Develops a calculation method for coherent information lower bounds on bipartite entanglement in graph states with pre-CZ depolarizing noise and identifies a family maintaining strictly positive coherent information for any non-maximal noise level.

References

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[1] Therefore, nB = 1 maximizes IA

[2] Given nB, IA is an increasing function of nA, which Asymptotically converges from below to a constant value for a given P ̸= 0 and P ̸= 1

[3] We show in Fig

[4] This gives H(ρA) = f1(1, P) = 1, with coherent information IA = 1 − nH2(P)

[5] When nA > nB, IA > IB and vice versa. That is, for any fully connected graph, the side hav- ing the largest number of qubits has the highest subsystem entropy (since f1(nA, P) > f1(nB, P) when nA > nB

Receipt and verification

First computed	2026-05-27T14:06:35.495954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a7b84351d5210502ca782a4cb5c607f04003fdb3d20e525ef0019adb4ca60c3

Aliases

arxiv: 2404.09014 · arxiv_version: 2404.09014v2 · doi: 10.48550/arxiv.2404.09014 · pith_short_12: TJ5YINI5KIIF · pith_short_16: TJ5YINI5KIIFALFH · pith_short_8: TJ5YINI5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TJ5YINI5KIIFALFHQKSMWXDAP4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9a7b84351d5210502ca782a4cb5c607f04003fdb3d20e525ef0019adb4ca60c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9436ddd295ddb861250822df70feed03c38917e79eaca7ffc7436d9b66a8d2b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2024-04-13T14:01:45Z",
    "title_canon_sha256": "29b13ccdb3933166c3913809deb04273292f62e181aab6e506fb983b88c85df2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.09014",
    "kind": "arxiv",
    "version": 2
  }
}