Pith Number

pith:3T7BV2KE

pith:2026:3T7BV2KEO6E7OXBJDVMMIVJNWC

not attested not anchored not stored refs pending

Operational interpretation of the reverse sandwiched Renyi divergences in composite quantum hypothesis testing

Kun Fang, Masahito Hayashi

The reverse sandwiched Renyi divergence exactly sets the optimal Hoeffding exponent for discriminating a thermal state from an unknown-dephased probe.

arxiv:2605.02203 v2 · 2026-05-04 · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3T7BV2KEO6E7OXBJDVMMIVJNWC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

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

for the task of discriminating a thermal equilibrium state from a probe state subject to unknown dephasing in the energy eigenbasis, with free Hamiltonian evolution as a special case, the optimal Hoeffding exponent is given exactly by this divergence evaluated on a single copy of the system.

C2weakest assumption

a set of structural assumptions on the composite hypotheses (sequences of sets of quantum states), stated to be orthogonal to those of the authors' previous framework; the abstract does not specify the precise form of these assumptions.

C3one line summary

The reverse sandwiched Renyi divergence for alpha in (0,1) exactly equals the optimal Hoeffding exponent for discriminating a thermal equilibrium state from a probe with unknown dephasing in the energy basis.

Formal links

3 machine-checked theorem links

Cited by

2 papers in Pith

A Quantum Method of Types

Receipt and verification

First computed	2026-06-08T01:04:06.411468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcfe1ae9447789f75c291d58c4552db08d6ba702a4dc9e67389bfda3b3adb309

Aliases

arxiv: 2605.02203 · arxiv_version: 2605.02203v2 · doi: 10.48550/arxiv.2605.02203 · pith_short_12: 3T7BV2KEO6E7 · pith_short_16: 3T7BV2KEO6E7OXBJ · pith_short_8: 3T7BV2KE

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/3T7BV2KEO6E7OXBJDVMMIVJNWC \
  | 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: dcfe1ae9447789f75c291d58c4552db08d6ba702a4dc9e67389bfda3b3adb309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60cc3b689af26a8ee8bbfe000e4f3bb2bbe337c624307322530c433fd266b4f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-04T04:02:55Z",
    "title_canon_sha256": "3295e7c4cc08ceb692b95096d3533d893a2b64b8e1569978601402d0fdf4540c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02203",
    "kind": "arxiv",
    "version": 2
  }
}