More Nonlocality with Less Entanglement in CHSH Experiments using Inefficient Detectors

Abstract

It is well-known that in certain scenarios weakly entangled states can generate stronger nonlocal effects than their maximally entangled counterparts. In this paper, we consider violations of the CHSH Inequality when one party has inefficient detectors, a scenario known as an asymmetric Bell experiment. %We show that violations can occur if and only if the detection efficiency is above $50\%$. For any fixed detection efficiency, we derive a simple upper bound on the entanglement needed to violate the inequality by more than some specified amount $\kappa \ge 0$. When $\kappa =0$, the amount of entanglement in all states violating the inequality goes to zero as the detection efficiency approaches $50\%$ from above. %This provides another scenario in which weakly entangled states are advantageous for violating the CHSH Inequality in the presence of detection inefficiency. We finally consider the scenario in which detection inefficiency arises for only one choice of local measurement. In this case, it is shown that the CHSH Inequality can always be violated for any nonzero detection efficiency and any choice of non-commuting measurements.

arXiv commentAdded references to pre-existing work and hence revised the language suggesting originality of certain findings; also strengthened Theorem 1

References in corpus (21)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Bell nonlocality
• Quantum non-locality in two three-level systems
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Entanglement versus Bell violations and their behaviour under local filtering operations
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• Large violation of Bell inequalities with low entanglement
• Entanglement and non-locality are different resources
• Detection loophole in asymmetric Bell experiments
• Minimum detection efficiency for a loophole-free atom-photon Bell experiment
• Semi-device-independent bounds on entanglement
• Quantum measurement incompatibility does not imply Bell nonlocality
• Measurement incompatibility does not give rise to Bell violation in general
• Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality
• Violation of local realism vs detection efficiency
• More non-locality with less entanglement
• There is no anomaly in the nonlocality of two entangled qutrits
• Exploring the limits of quantum nonlocality with entangled photons
• Bell scenarios in which nonlocality and entanglement are inversely related

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