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arXiv:1806.08923 · Physics Letters B

Bell inequalities violation within non-Bunch–Davies states

Jun Feng, Xiaoyang Huang, Yao-Zhong Zhang, Heng Fan

Published Oct 16, 2018• 17 citations
arXivHTMLPDF

Abstract

In this Letter, we study the quantum nature of non-Bunch–Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons–Hawking temperature, the CHSH bound degrades monotonously for Bunch–Davies vacuum sector. Due to the intrinsic correlation of non-Bunch–Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch–Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space.

DOI
10.1016/j.physletb.2018.10.020

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In this Letter, we study the quantum nature of non-Bunch–Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons–Hawking temperature, the CHSH bound degrades monotonously for Bunch–Davies vacuum sector. Due to the intrinsic correlation of non-Bunch–Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch–Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space.
Quantum systems are inherently open and fragile, leading to the loss of information and quantum properties to the environment. This study investigates the behavior of quantum entanglement (QE), quantum nonlocality (QN), and measurement uncertainty in a two-atom system interacting with a common dissipative thermal reservoir under the Markovian approximation. QE is measured using concurrence, QN through the CHSH-Bell inequality, and uncertainty through the quantum memory-assisted entropic uncertainty relation (QMA-EUR). The findings show that both QE and QN decay as the scaled time and excitation numbers increase, with QE being more resilient. In contrast, QMA-EUR shows an anticorrelation with concurrence and CHSH-Bell violation, increasing as these properties diminish. Adjusting the system initial-state parameters improves QE and CHSH degree of violation, while reducing uncertainty. Over long durations, concurrence and CHSH-Bell violations disappear, while QMA-EUR stabilizes at its maximum value. These results highlight the importance of precise parameter control to enhance quantum features and predict outcomes, especially for bipartite systems initialized in a Werner-like state.
We study the violation of Bell-Mermin-Klyshko (BMK) inequalities in initial quantum states of scalar fields in inflation. We show that the Bell inequality is maximally violated by the Bunch-Davies vacuum which is a two-mode squeezed state of a scalar field. However, we find that the violation of the BMK inequalities does not increase with the number of modes to measure. We then consider a non-Bunch-Davies vacuum expressed by a four-mode squeezed state of two scalar fields. Remarkably, we find that the violation of the BMK inequalities increases exponentially with the number of modes to measure. This shows that the BMK inequalities are useful to classify the initial quantum state of the Universe.
In solid-state systems, spin squeezing states have acquired much interest in quantum information processing since they are not only essential from a basic physics standpoint but also have many applications, notably reducing noise in interferometry. This paper addresses the study of quantum nonlocality as examined by the violation of the Bell and Clauser–Horne–Shimony–Holt (CHSH) inequality in two classes of spin squeezing states and how this relates to the quantum-memory-assisted entropic uncertainty relation (QMA–EUR). The spin squeezing states in the two classes are systematically generated by two twisting nonlinear interactions. These separately describe two spin-[Formula: see text] interaction mechanisms that undergo one-axis twisting (OAT) and two-axis countertwisting (TAC). We investigate each spin squeezing mechanism in a thermal bath ([Formula: see text]) with a transverse magnetic field. Our main results indicate that the degree of violation of the Bell-CHSH inequality and the entropic uncertainty relation (EUR) is typically anticorrelated in both mechanisms. We demonstrate that the spin squeezing states in the OAT mechanism violate the Bell-CHSH inequality and thus exhibit Bell nonlocality only at low temperatures ([Formula: see text]), whereas in the TAC mechanism, increasing the strength of the spin squeezing interaction leads to a violation of the Bell-CHSH inequality even at finite temperatures. We have also shown that there is always an expansion of the EUR and a decrease in the degree of violation of the Bell-CHSH inequality in the high-temperature regime. In addition, the transverse magnetic field exhibits different behavior under the considered temperature regimes in the two classes of spin squeezing states. Other results will also be discussed.
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.
Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of 222\sqrt{2}22​. Although Bell's wave function does not produce a large violation of the CHSH inequality, other states may yet do so.
Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by the violation of certain inequalities, the simplest and most important of which are the Clauser-Horne-Shimony-Holt (CHSH) and the Klyachko-Can-Binicioğlu-Shumovski (KCBS), for Bell nonlocality and Kochen-Specker contextuality, respectively. It has been shown that, using the most common interpretation of Bell scenarios, quantum systems cannot violate both inequalities concomitantly, thus suggesting a monogamous relation between the two phenomena. In this Letter, we show that the joint consideration of the CHSH and KCBS inequalities naturally calls for the so-called generalized Bell scenarios, which, contrary to the previous results, allows for joint violation of them. In fact, this result is not a special feature of such inequalities: We provide very strong evidence that there is no monogamy between nonlocality and contextuality in any scenario where both phenomena can be observed. We also implement a photonic experiment to test the synchronous violation of both CHSH and KCBS inequalities. Our results agree with the theoretical predictions, thereby providing experimental proof of the coexistence of Bell nonlocality and contextuality in the simplest scenario, and lead to novel possibilities where both concepts could be jointly employed for quantum information processing protocols.