Pith Number

pith:KWEQIC5B

pith:2026:KWEQIC5BX3Q3SVUACTH2HNHULY

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A universal complementarity identity for polarized double-slit interferometry

Jos\'e J. Gil

Four measurable quantities in polarized double-slit experiments satisfy the exact identity V_A squared plus V_N squared plus P squared plus I squared equals one.

arxiv:2604.18760 v2 · 2026-04-20 · quant-ph · physics.optics

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Claims

C1strongest claim

We establish an exact identity among four dimensionless invariants ... V_A^2 + V_N^2 + P^2 + I^2 = 1. The identity is a universal algebraic consequence of the positivity of the reduced state and holds for every normalized path-polarization density matrix.

C2weakest assumption

The reduced path-polarization density matrix is positive semidefinite (a standard quantum-mechanical requirement) and normalized; if this fails for the physical system under study the identity would not hold.

C3one line summary

In polarized double-slit interferometry the sum of the squares of in-phase visibility, quadrature visibility, path predictability, and path-state mixedness equals one for any normalized density matrix.

Cited by

1 paper in Pith

Intrinsic Pointer Basis and Irreversible Classicality from Coherence Contraction

Receipt and verification

First computed	2026-06-01T01:03:53.453671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5589040ba1bee1b9568014cfa3b4f45e3e52768e19cb79d4de1ed60fcfaa3f69

Aliases

arxiv: 2604.18760 · arxiv_version: 2604.18760v2 · doi: 10.48550/arxiv.2604.18760 · pith_short_12: KWEQIC5BX3Q3 · pith_short_16: KWEQIC5BX3Q3SVUA · pith_short_8: KWEQIC5B

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KWEQIC5BX3Q3SVUACTH2HNHULY \
  | 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: 5589040ba1bee1b9568014cfa3b4f45e3e52768e19cb79d4de1ed60fcfaa3f69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19c5c0f24218f5bd6841c156ad9be53dc9f495fa83a8b0e48fc54330721ef124",
    "cross_cats_sorted": [
      "physics.optics"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-20T19:09:51Z",
    "title_canon_sha256": "5ea3f2e327a24f2a5fc2613ed5c215c58775d27727d11d44c51334b5b35b9593"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18760",
    "kind": "arxiv",
    "version": 2
  }
}