Pith Number

pith:DXA5PGA4

pith:2026:DXA5PGA4YOTCMXPW7TDFPFEEYI

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Localization of joint quantum measurements on $\mathbb{C}^d \otimes \mathbb{C}^d$ by entangled resources with Schmidt number at most $d$

Jisho Miyazaki, Seiseki Akibue

A rank-1 joint measurement on two d-dimensional systems can be localized with entanglement of Schmidt number at most d if and only if its elements form a maximally entangled basis from a nice unitary error basis.

arxiv:2601.02660 v2 · 2026-01-06 · quant-ph

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\pithnumber{DXA5PGA4YOTCMXPW7TDFPFEEYI}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

a rank-1 PVM on C^d ⊗ C^d containing an element with the maximal Schmidt rank can be localized using entanglement of a Schmidt number at most d if and only if it forms a maximally entangled basis corresponding to a nice unitary error basis

C2weakest assumption

The PVM must be rank-1 and contain at least one element of maximal Schmidt rank; the characterization is stated only under this restriction and may not extend without it.

C3one line summary

Rank-1 PVMs on two qudits with a maximal-Schmidt-rank element are localizable with Schmidt number at most d exactly when they correspond to nice unitary error bases; the two-qubit case is fully classified, resolving a prior conjecture.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] and partially entangled bases, such as { |00⟩, |11⟩, |01⟩ + |10⟩ √ 2 , |01⟩ − |10⟩√ 2 } (named “pBSM” in [14]). Among iso-entangled bases, the higher-dimensional generalization [27] of the elegant joi

[2] ideal measurement

[3] which subspace

[4] N. Gisin and F. Del Santo, Towards a measurement the- ory in QFT: ”Impossible” quantum measurements are possible but not ideal, Quantum 8, 1267 (2024) 2024

[5] Y. Aharonov and D. Z. Albert, States and ob- servables in relativistic quantum ﬁeld theories, Phys. Rev. D 21, 3316 (1980) 1980

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:16.721291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dc1d7981cc3a6265df6fcc6579484c205875300350ee5fdf5e474ad9cdf50ef

Aliases

arxiv: 2601.02660 · arxiv_version: 2601.02660v2 · doi: 10.48550/arxiv.2601.02660 · pith_short_12: DXA5PGA4YOTC · pith_short_16: DXA5PGA4YOTCMXPW · pith_short_8: DXA5PGA4

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/DXA5PGA4YOTCMXPW7TDFPFEEYI \
  | 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: 1dc1d7981cc3a6265df6fcc6579484c205875300350ee5fdf5e474ad9cdf50ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f75d6c01112213d06f1295d807c7fee95fddb8fc04336e38b36e1a1dfa40a8a3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-01-06T02:18:17Z",
    "title_canon_sha256": "5117b306a45984b55486ef324f84be7cbe4bf08995744132398900a6a4a28eb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.02660",
    "kind": "arxiv",
    "version": 2
  }
}