Bell-Inequality Violation for Continuous, Non-Projective Measurements

• URL: http://arxiv.org/abs/2512.22229v1
• Date: Tue, 23 Dec 2025 03:58:54 GMT
• Title: Bell-Inequality Violation for Continuous, Non-Projective Measurements
• Authors: Shalender Singh, Santosh Kumar,
• Abstract summary: We show that Bell-CHSH inequality violation can be extracted from continuous, non-projective measurements.<n>We benchmark the resulting estimator against conventional projective-measurement CHSH tests.<n>Our results provide a practical route to demonstrating Bell nonlocality in platforms where measurements are inherently continuous and weak.
• Score: 1.5755923640031846
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many solid-state quantum platforms do not permit sharp, projective measurements but instead yield continuous voltage or field traces under weak, non-demolition readout. In such systems, standard Bell tests based on dichotomic projective measurements are not directly applicable, raising the question of how quantum nonlocality can be certified from continuous time-series data. Here we develop a general theoretical framework showing that Bell-CHSH inequality violation can be extracted from continuous, non-projective measurements without assuming any specific collapse model or phase distribution. We show that sufficiently long continuous measurements of a single entangled pair sample its internal phase-probability structure, enabling effective dichotomic observables to be constructed through phase-sensitive projections and coarse-graining. The resulting Bell correlator is governed by two experimentally accessible resources: intrinsic single-qubit phase spread and nonlocal phase locking between qubits. We benchmark the resulting estimator against conventional projective-measurement CHSH tests implemented via quantum-circuit simulations using Qiskit, finding quantitative agreement in the Bell-violating regime without parameter fitting. Classical deterministic correlations cannot violate the CHSH bound, whereas quantum phase-locked systems recover the nonlinear angular dependence characteristic of entanglement. Our results provide a practical route to demonstrating Bell nonlocality in platforms where measurements are inherently continuous and weak.

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