bibkey: gisin2017elegantjointmeasurement
authors: Nicolas Gisin
year: 2017
title: The Elegant Joint Quantum Measurement and some conjectures about N-locality in the Triangle and other Configurations
doi: null
url: https://arxiv.org/abs/1708.05556
claim: The elegant joint measurement and its singlet-triangle distribution are the physical literature inputs; the sourcewise noisy Born polynomial is verified separately in Lean.
strata_touched:
  - D5/S3/Quantum/Entanglement/ElegantJointMeasurementSourceNoise
license: citation-only
triage: anchor

Elegant joint measurement in a singlet triangle

Gisin’s elegant joint measurement, Section II, equation (11), is the physical input for the four-outcome two-qubit measurement in ElegantJointMeasurementSourceNoise. The four tetrahedral directions specify a common singlet component and three Cartesian triplet components. In the computational basis, the unnormalized vectors have entries sx + i sy, sz + 1, sz - 1, and -sx + i sy; the effects are their outer products multiplied by 1/8.

Section III, equations (12)–(14), uses three independent singlet sources and the cyclic outgoing/incoming wire order at each party. The outcome probabilities are 25/256 when all labels agree, 1/256 when exactly two agree, and 5/256 when all differ. Neither this table nor a physical quantum realization alone proves classical triangle incompatibility.

The Lean module constructs positive normalized density matrices and local POVMs and derives the exact polynomial when the three sources are independently mixed with I/4. Its three visibilities belong to the source matrices before the tensor Born rule. The formal polynomial identity is not attributed as a new physical measurement, and independent source noise is not identified with a global mixture of the final output table.

Verified locator

The original PDF at https://arxiv.org/abs/1708.05556, version v1 submitted 18 August 2017, identifies Nicolas Gisin and the title above. Page 2 contains the EJM construction in Section II, equation (11), and the triangle table in Section III, equations (12)–(14). The source proposes nonlocality as a conjecture without proof; it is not a nonlocality certificate. The matrix identities and noisy probability values claimed by this module are checked separately from its explicit Lean definitions.