Pith Number

pith:BYOAAHKF

pith:2026:BYOAAHKFLLCJUY7H4HHZD4AOCJ

not attested not anchored not stored refs resolved

Quantum Fractional Revival and Entanglement Entropy in Unitary Cayley Graphs

Duaa Abdullah

Unitary Cayley graphs of order twice an odd prime exhibit quantum fractional revival at time 2π/p with amplitudes cos(2π/p) and -i sin(2π/p).

arxiv:2605.13645 v1 · 2026-05-13 · math.CO · math.SP

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\pithnumber{BYOAAHKFLLCJUY7H4HHZD4AOCJ}

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4 Citations open

5 Replications open

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Claims

C1strongest claim

For unitary Cayley graphs of order n=2p where p is an odd prime, the minimum revival time is t^*=2π/p with revival amplitudes α=cos(2π/p), β=-i sin(2π/p); the von Neumann entanglement entropy depends solely on |α| and |β|.

C2weakest assumption

The graphs must be unitary Cayley graphs on Z_n with the arithmetic structure allowing the closed-form spectral analysis; the equivalence of adjacency and Laplacian Hamiltonians holds only for regular graphs.

C3one line summary

For unitary Cayley graphs of order 2p with p odd prime, minimum quantum fractional revival time is 2π/p with amplitudes cos(2π/p) and -i sin(2π/p); entanglement entropy depends only on the absolute values of these amplitudes.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] Quantum fractional revival in unitary Cayley graphs, 1922

[2] Quantum fractional revival on graphs, 2019

[3] Fundamentals of fractional revival in graphs, 2022

[4] Laplacian fractional revival on graphs, 2021

[5] Pretty good quantum fractional revival in paths and cycles, 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:17.552267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e1c001d455ac49a63e7e1cf91f00e12558dac18171217c3b1ce6d52b799701d

Aliases

arxiv: 2605.13645 · arxiv_version: 2605.13645v1 · doi: 10.48550/arxiv.2605.13645 · pith_short_12: BYOAAHKFLLCJ · pith_short_16: BYOAAHKFLLCJUY7H · pith_short_8: BYOAAHKF

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BYOAAHKFLLCJUY7H4HHZD4AOCJ \
  | 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: 0e1c001d455ac49a63e7e1cf91f00e12558dac18171217c3b1ce6d52b799701d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f63daac2a68f0e2ca59c68e1d3e568d91d4cb4cf0464f193fecb1bac698db4c1",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T15:06:11Z",
    "title_canon_sha256": "72e972de6499afc92332b4213f20440b5f163ea8042cc8bf055cd89aaf9d4ae2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13645",
    "kind": "arxiv",
    "version": 1
  }
}