Quantum Nonlocality and Device-Independent Randomness Robust to Relaxations of Bell Assumptions

• URL: http://arxiv.org/abs/2512.18513v1
• Date: Sat, 20 Dec 2025 21:20:18 GMT
• Title: Quantum Nonlocality and Device-Independent Randomness Robust to Relaxations of Bell Assumptions
• Authors: Ravishankar Ramanathan, Yuan Liu,
• Abstract summary: We show that states of constant local dimension $d$ are sufficient to certify quantum nonlocality under arbitrary MI and PI relaxation.<n>We introduce the notion of textitmeasurement-dependent locality as the set of input-output behaviors under simultaneous relaxations of measurement and independence.<n>We analytically derive the quantum guessing probability for one player's outcomes in the CHSH Bell test.
• Score: 4.183295888979239
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The question of certifying quantum nonlocality under a relaxation of the assumptions in the Bell theorem has gained traction, with potential for device-independent applications under weak seeds and cross-talk. Recently, it was shown that quantum nonlocality can be certified even under a simultaneous arbitrary (but not full) relaxation of the assumptions of Measurement Independence (MI) and Parameter Independence (PI), using states of local dimension $d = poly((1-ε)^{-1})$ for an $ε\in [0,1)$-relaxation. Here, we derive three results strengthening the state-of-art. Firstly, we show that states of constant local dimension $d$ are already sufficient to certify quantum nonlocality under arbitrary MI and PI relaxation, albeit in a non-robust manner. Secondly, and as a theoretical paradigm to derive the above, we introduce the notion of \textit{measurement-dependent parameter-dependent locality} as the set of input-output behaviors under simultaneous relaxations of measurement and parameter independence. We provide a rigorous characterisation of the vertices of the polytope of joint input-output behaviors that obey a $μ$-relaxation of MI and $ε$-relaxation of PI. We highlight a relation between nonlocality certification under PI relaxation and that under detection inefficiencies by pointing out alternative extremal correlations to the Eberhard correlations that also allow to achieve detection efficiency of $η= 2/3$ in the two-input scenario. Finally, we study the implication of the relaxed assumptions for device-independent randomness certification. We analytically derive the quantum guessing probability for one player's outcomes in the CHSH Bell test, as a function of the noise in the test as well as of a leakage of an average amount of $I(X:B) < 1$ bits of input information per measurement round.

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