Pith Number

pith:SZ6YCFAF

pith:2025:SZ6YCFAF4CQPFNYEXWTTWIABVR

not attested not anchored not stored refs resolved

Quantum Advantage in Storage and Retrieval of Isometry Channels

Jisho Miyazaki, Mio Murao, Satoshi Yoshida

Quantum strategies store unknown isometry channels using only the square root as many queries as classical estimation.

arxiv:2507.10784 v4 · 2025-07-14 · quant-ph

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\pithnumber{SZ6YCFAF4CQPFNYEXWTTWIABVR}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

The optimal fidelity for isometry estimation is F = 1 - d(D-d)/n + O(n^{-2}), showing classical strategy requires n = Θ(ε^{-1}) while the proposed quantum strategy achieves n = Θ(1/√ε) for diamond-norm error ε.

C2weakest assumption

The analysis assumes multiple independent queries to the fixed but unknown isometry channel are available and that the large-n asymptotic regime governs the error scaling.

C3one line summary

Quantum strategy stores isometry channels with n = Θ(1/√ε) queries for error ε, quadratic improvement over classical n = Θ(ε^{-1}).

References

101 extracted · 101 resolved · 37 Pith anchors

[1] Isometry operatorV∈V iso(d, D) is defined by ad×Dcomplex matrix satisfyingV †V=1 d, which is given byd 2 independent conditions on real param- eters

[2] ,|v d⟩} ⊂C D

[3] Definition of the Young diagrams 6

[4] Schur-Weyl duality 7

[5] Review on quantum testers 10

Formal links

2 machine-checked theorem links

Cited by

3 papers in Pith

Random dilation superchannel

Strict Hierarchy for Quantum Channel Certification to Unitary

Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition

Receipt and verification

First computed	2026-06-01T01:02:17.467773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

967d811405e0a0f2b704bda73b2001ac462e2ad3695194a192705982efced7aa

Aliases

arxiv: 2507.10784 · arxiv_version: 2507.10784v4 · doi: 10.48550/arxiv.2507.10784 · pith_short_12: SZ6YCFAF4CQP · pith_short_16: SZ6YCFAF4CQPFNYE · pith_short_8: SZ6YCFAF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SZ6YCFAF4CQPFNYEXWTTWIABVR \
  | 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: 967d811405e0a0f2b704bda73b2001ac462e2ad3695194a192705982efced7aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "125580107ee0ba9c5919ee05a447412f84e10c0fc143c55a57152b312928c27f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-07-14T20:18:12Z",
    "title_canon_sha256": "79fb8c3e21d7f27976aa982ce9fcdf6d13a15bef6fab4d14432a426d16889590"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.10784",
    "kind": "arxiv",
    "version": 4
  }
}