The measurement postulates of quantum mechanics are operationally redundant

The question of how Bell nonlocality behaves in bipartite systems of higher dimensions is addressed. By employing the probability of violation of local realism under random measurements as the figure of merit, we investigate the nonlocality of entangled qudits with dimensions ranging from d = 2 to d = 7. We proceed in two complementary directions. First, we study the specific Bell scenario defined by the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality. Second, we consider the nonlocality of the same states under a more general perspective, by directly addressing the space of joint probabilities (computing the frequencies of behaviours outside the local polytope). In both approaches we find that the nonlocality decreases as the dimension d grows, but in quite distinct ways. While the drop in the probability of violation is exponential in the CGLMP scenario, it presents, at most, a linear decay in the space of behaviours. Furthermore, in both cases the states that produce maximal numeric violations in the CGLMP inequality present low probabilities of violation in comparison with maximally entangled states, so, no anomaly is observed. Finally, the nonlocality of states with non-maximal Schmidt rank is investigated.

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“…where ⊕ denotes sum modulo d. The corresponding CGLMP inequality is a facet of the associated local polytope [39] and reads:…”

Section: A Multiport Beam Splitters and Phase Shiftersmentioning

confidence: 99%

Survey on the Bell nonlocality of a pair of entangled qudits

et al. 2018

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“…Deriving the constraint that maximizes N such that N is larger than the dimension of the local bound can be an analytic approach to tighten a Bell's inequality. As the condition is the necessary condition for a Bell's inequality to be tight [25].…”

Section: B Local Realistic Upper Boundmentioning

confidence: 99%

Generalized nonlocality criteria under the correlation symmetry

Bae

Son

2018

Phys. Rev. A

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The most general class of non-locality criteria for N -partite d-chotomic systems with k number of measurement settings is derived under the constraint of measurement symmetries. It is the complete characterisation of the multi-partite non-locality when the correlation is assumed to be symmetric under the choice of measurement settings. The generalized non-locality condition is obtained using the correlation functions, which are derived from Fourier analysis of probability spectrums. It is found that the condition for the local hidden variable (LHV) model is violated by multipartite quantum states and general constraints for the quantum violation of maximally entangled state has been obtained.

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“…Zurek has suggested decoherence as an explanation of the Born rule [17], although this view has been criticized as well to be insufficient [18]. More recently, Masanes et al have claimed to derive the Born rule by assuming, among other things, that measurements consist of well-defined trials and always produce one of a pre-defined set of outcomes [19]. While seemingly innocuous, this assumption does not always hold in real, experimental settings where, for example, photons are detected at random times or, more often, not at all.…”

Section: Introductionmentioning

confidence: 99%

Emergence of the Born rule in quantum optics

Cour

Williamson

2020

Quantum

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The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the assumption of a quantum electrodynamic vacuum that is real rather than virtual. The connection to observation is made via classical intensity threshold detectors that are used as a simple, deterministic model of photon detection. By following standard experimental conventions of data analysis on discrete detection events, we show that this model is capable of reproducing several observed phenomena thought to be uniquely quantum in nature, thus providing greater elucidation of the quantum-classical boundary.

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The measurement postulates of quantum mechanics are operationally redundant

Cited by 59 publications

References 41 publications

Survey on the Bell nonlocality of a pair of entangled qudits

Survey on the Bell nonlocality of a pair of entangled qudits

Generalized nonlocality criteria under the correlation symmetry

Emergence of the Born rule in quantum optics

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