Pith Number

pith:VPHS7GOH

pith:2026:VPHS7GOHHC37SPNKFCWCUMARPP

not attested not anchored not stored refs resolved

Exact Entanglement-Depth Speed Frontier for Complete Quantum Charging

Gang Lu, Wenlong Sun, Yuanfeng Jin

If a quantum battery charges with normalized rate η, its trajectory must involve entanglement depth at least ceil(N / floor(1/η²)).

arxiv:2605.16935 v1 · 2026-05-16 · quant-ph · math.OA

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

If the realized trajectory has entanglement depth at most k, then the largest possible QSL-normalized rate η=τ_QSL/T is η_max(k)=⌈N/k⌉^{-1/2}. Conversely, an observed rate η certifies trajectory entanglement depth at least ⌈N/⌊η^{-2}⌋⌉.

C2weakest assumption

Under a fixed product partition into blocks of size at most k, complete charging forces all blocks to orthogonalize simultaneously, allowing the quantum speed limit to convert the resulting counting constraint into the speed bound (abstract mechanism paragraph).

C3one line summary

For N-qubit complete charging from all-down to all-up under time-independent Hamiltonians, the maximum QSL-normalized rate with entanglement depth ≤k is exactly 1/sqrt(ceil(N/k)), saturated by balanced cluster-flip evolutions and enabling certification of genuine N-partite entanglement for rates >1/

References

28 extracted · 28 resolved · 0 Pith anchors

[1] The certified depth therefore increases in inte- ger steps as the charging time approaches the QSL 2025

[2] Entanglement boost for ex- tractable work from ensembles of quantum batteries, 2013

[3] Quantacell: Powerful charging of quantum batteries, 2015

[4] Enhancing the charging power of quantum batteries, 2017

[5] High-power collective charging of a solid- state quantum battery, 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:31.686870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abcf2f99c738b7f93daa28ac2a30117be3ca1659fd27d3c59799433cd5d11883

Aliases

arxiv: 2605.16935 · arxiv_version: 2605.16935v1 · doi: 10.48550/arxiv.2605.16935 · pith_short_12: VPHS7GOHHC37 · pith_short_16: VPHS7GOHHC37SPNK · pith_short_8: VPHS7GOH

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VPHS7GOHHC37SPNKFCWCUMARPP \
  | 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: abcf2f99c738b7f93daa28ac2a30117be3ca1659fd27d3c59799433cd5d11883

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a61be2b2d69c93ce97d4b573e434662a63803835bc5bb896a57aa62c6aece024",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-16T11:08:17Z",
    "title_canon_sha256": "278a42d39eda002ae9d16544c68da5c34cdee650a1175b935a2fa6735feb8178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16935",
    "kind": "arxiv",
    "version": 1
  }
}