Bell Nonlocality Research Articles

Quantum nonlocality of density operators and their corresponding density matrices

Abstract Quantum nonlocality represents correlations between subsystems of a composite quantum system, usually including Bell nonlocality, steerability, and entanglement. According to the hypothesis of quantum mechanics, states of a quantum system $Q$ described by a $d$-dimensional Hilbert space $\H_Q$ are denoted by density operators acting on $\H_Q$. Under a basis $e$ for the Hilbert space $\H_A\otimes \H_B$, every abstract density operator $\rho$ of the system $AB$ corresponds to a density matrix ${\rho}_{e}$, which is a state of the {$d_Ad_B$-dimensional complex Hilbert space } $\C^{d_A}\otimes\C^{d_B}$. In this work, we discuss the consistency of
 quantum nonlocality of density operators $\rho$ and their corresponding density matrices ${\rho}_e$ under the chosen basis $e$. It is proved that only when a basis $e$ is a product one, a density operator $\rho$ is entangled (resp., Bell nonlocal, steerable) if and only if its density matrix ${\rho}_e$ is entangled (resp., Bell nonlocal, steerable).

Entanglement, quantum steering, and Bell nonlocality in the Tavis–Cummings system

In this work, we focus on quantum correlations, specifically entanglement, quantum steering, and Bell nonlocality within the Tavis–Cummings model. This study investigates these quantum correlations in the context of various fields existing in the cavity. The findings reveal the hierarchy of quantum correlations—entanglement, quantum steering, and Bell nonlocality—in two two-level atoms under the influence of thermal, coherent, and squeezed vacuum states. The dynamic process demonstrates certain oscillations, with particular emphasis on the presence of asymmetric quantum steering.

Deterministic all-versus-nothing proofs of bell nonlocality induced from qudit non-stabilizer states

Recently, a type of deterministic all-versus-nothing proofs of Bell nonlocality, induced from qubit non-stabilizer states, was proposed, diverging from the tradition where such proofs are typically derived from stabilizer states. Moreover, through the application of a specific map, one can derive certain trivial (dimensionally reducible) versions of such proofs for qudits (d being even). Nevertheless, it remains unknown whether high-dimensional non-stabilizer states can induce nontrivial deterministic all-versus-nothing proofs of Bell nonlocality. In this study, we provide an example induced from a specific four-qudit non-stabilizer state (with d=4), demonstrating the feasibility of constructing such proofs in high-dimensional scenarios.

SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness

Bell non-locality is closely related with device independent quantum randomness. In this paper, we present a kind of sum-of-squares (SOS) decomposition for general Bell inequalities in two qubits systems. By using the obtained SOS decomposition, we can then find the measurement operators associated with the maximal violation of considered Bell inequality. We also practice the SOS decomposition method by considering the (generalized) Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, the Elegant Bell inequality, the Gisin inequality and the Chained Bell inequality as examples. The corresponding SOS decompositions and the measurement operators that cause the maximum violation values of these Bell inequalities are derived, which are consistent with previous results. We further discuss the device independent quantum randomness by using the SOS decompositions of Bell inequalities. We take the generalized CHSH inequality with the maximally entangled state and the Werner state that attaining the maximal violations as examples. Exact value or lower bound on the maximal guessing probability using the SOS decomposition are obtained. For Werner state, the lower bound can supply a much precise estimation of quantum randomness when p tends to 1.

Effects of topological boundary conditions on Bell nonlocality

Effects of topological boundary conditions on Bell nonlocality

Sharing asymmetric Einstein–Podolsky–Rosen steering with projective measurements

Recently, both global and local classical randomness-assisted projective measurement protocols have been employed to share Bell nonlocality of an entangled state among multiple sequential parties. Unlike Bell nonlocality, Einstein–Podolsky–Rosen (EPR) steering exhibits distinct asymmetric characteristics and serves as the necessary quantum resource for one-sided device-independent quantum information tasks. In this work, we propose a projective measurement protocol and investigate the shareability of EPR steering with steering radius criterion theoretically and experimentally. Our results reveal that arbitrarily many independent parties can share one-way steerability using projective measurements, even when no shared randomness is available. Furthermore, by leveraging only local randomness, asymmetric two-way steerability can also be shared. Our work not only deepens the understanding of the role of projective measurements in sharing quantum correlations but also opens up a new avenue for reutilizing asymmetric quantum correlations.

Trade-off relations between Bell nonlocality and local Kochen–Specker contextuality in generalized Bell scenarios

Trade-off relations between Bell nonlocality and local Kochen–Specker contextuality in generalized Bell scenarios

Does gravitational wave assist vacuum steering and Bell nonlocality?

We study quantum steering and Bell nonlocality harvested by the local interaction of two Unruh-DeWitt detectors with the vacuum massless scalar field, both in the presence of gravitational waves and in Minkowski spacetime. It is shown that quantum steerability under the influence of gravitational waves can be greater than or less than quantum steerability in Minkowski spacetime, which means that the gravitational waves can amplify or degrade the harvested steering. In particular, a resonance effect occurs when the energy gap of the detector is tuned to the frequency of the gravitational wave. We also find that the harvesting-achievable separation range of vacuum steering can be expanded or reduced by the presence of gravitational waves, which depends on the energy gap, the gravitational wave frequency, and the duration of the gravitational wave action. It is interesting to note that two detector systems that satisfy the Bell inequality in most parameter spaces, regardless of the existence of gravitational waves, indicating that steering harvesting cannot be considered to be nonlocal.

Quantumness of gravitational cat states in correlated dephasing channels

We study the quantumness of gravitational cat states in correlated dephasing channels. Our focus is on exploring how classical correlations between successive actions of a dephasing channel influence the decoherence of two gravitational cats (two qubits) at a thermal regime. The results show that the quantum coherence, local quantum Fisher information, and Bell non-locality can be significantly enhanced by augmenting classical correlations throughout the entire duration when the two qubits pass the channel. However, the gravitational interaction and energy gap between states exhibit intricate impacts on the quantum characteristics of gravitational cats. New features are reported that can be significant for both gravitational physics and quantum information processing.

Compatibility of Generalized Noisy Qubit Measurements.

It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine the critical visibility such that all qubit measurements, i.e., all positive operator-valued measures (POVMs), become compatible, i.e., jointly measurable. In addition, we apply our methods to quantum steering and Bell nonlocality. We obtain a tight local hidden state model for two-qubit Werner states of visibility 1/2. This determines the exact steering bound for two-qubit Werner states and also provides a local hidden variable model that improves on previously known models. Interestingly, this proves that POVMs are not more powerful than projective measurements to demonstrate quantum steering for these states.

Exact Steering Bound for Two-Qubit Werner States.

Whether positive operator-valued measures (POVMs) provide advantages in demonstrating Bell nonlocality has remained unknown, even in the simple scenario of Einstein-Podolsky-Rosen steering with noisy singlet state, known as Werner states. Here we resolve this long-standing open problem by constructing a local hidden state model for Werner states with any visibility r≤1/2 under general POVMs, thereby closing the so-called Werner gap. This construction is based on an exact measurement compatibility model for the set of all noisy POVMs and also provides a local hidden variable model for a larger range of Werner states than previously known.

Research on quantum correlations and Uhlmann phase in two-fermion mixed state system

Geometric phase, characterized by its unique properties has been an interesting subject since the discovery of Berry phase. A state inevitably becomes a mixed state in the environment. Uhlmann phase can be applied to mixed states and may be the generalization of Berry phase. In this paper, we use a pair of interacting spin-1/2 fermions, where one particle is influenced by an external magnetic field, while the other remains unaffected, to investigate quantum correlations and Uhlmann phase, we define g, p as the ratio of the particle coupling intensity to the magnetic field, and q as the depolarization parameter. Through calculation, we get the specific parameter range q of steering and Bell nonlocality under the depolarized noise channel, q∈0,1−4+g24+2g2 (steering) and q∈0,1−4+g24+3g2 (Bell nonlocality). Moreover, by using Uhlmann phase, we obtain a simple discrimination criterion of the steerability (Bell nonlocality) of the mixed system.

Tripartite entanglement and Bell non-locality in loop-induced Higgs boson decays

In this article, we study quantum entanglement properties of the three-body H→γll¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H\\rightarrow \\gamma l{\\bar{l}}$$\\end{document} decays (for l=e,μ,τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l=e,\\mu ,\ au $$\\end{document}) within the context of the Standard Model augmented with CP-violating interactions in the lepton Yukawa sector. Our aim is to elucidate the distribution of entanglement between the final photon, lepton and antilepton across the phase-space. These rare Higgs boson decays occur at 1-loop level, presenting a unique opportunity to scrutinize quantum correlations of fundamental interactions in tripartite systems by computing concurrence measures and investigating Bell non-locality. Moreover, we explore post-decay and autodistillation phenomena. Multipartite entanglement measures have much richer structure than those in the bipartite case, thus deserve more attention in collider phenomenology. In this line, we analyze here novel observables for these three-body Higgs boson decays, which can be extended to other multiparticle systems within the high-energy regime. We found that entanglement manifests among final particles, occasionally achieving a maximally entangled state in specific kinematical configurations. Also, these decay channels are promising for Bell non-locality tests but CP-effects are suppressed by lepton masses in this kind of observables.

Detecting Bell nonlocality based on weak Hardy-like paradoxes and Hardy-Bell inequalities

Detecting Bell nonlocality based on weak Hardy-like paradoxes and Hardy-Bell inequalities

Quantum correlations in a chain-type quantum network

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some observers. In this paper, we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameter λ. The expressions of all post-measurement states between any two observers are obtained, and their quantifications of Bell nonlocality, Einstein–Podolsky–Rosen steering and entanglement with different ranges of λ are respectively detected and analyzed.

Bell Nonlocality in Classical Systems Coexisting with Other System Types.

The realistic interpretation of classical theory assumes that every classical system has well-defined properties, which may be unknown to the observer but are nevertheless part of reality and can, in principle, be revealed by measurements. Here we show that this interpretation can, in principle, be falsified if classical systems coexist with other types of physical systems. To make this point, we construct a toy theory that (i)includes classical theory as a subtheory and (ii)allows classical systems to be entangled with another type of system, called anticlassical. We show that our toy theory allows for the violation of Bell inequalities in two-party scenarios where one of the settings corresponds to a local measurement performed on a classical system alone. Building on this fact, we show that measurement outcomes in classical theory cannot, in general, be regarded as predetermined by the state of an underlying reality.

All-optical Einstein-Podolsky-Rosen steering swapping.

Einstein-Podolsky-Rosen (EPR) steering, an important resource in quantum information, describes the ability of one party to influence the state of another party through local measurements. It differs from Bell nonlocality and entanglement due to its asymmetric property. EPR steering swapping allows two spatially independent parties to present EPR steering without direct interaction. Here, we theoretically propose an all-optical EPR steering swapping (AOSS) scheme based on low-noise high-broadband optical parametric amplifiers (OPAs). A low-noise high-broadband OPA is utilized to implement the function of Bell-state measurement without detection, avoiding the optic-electro and electro-optic conversions. After AOSS, one-way and two-way EPR steering between two independent optical modes can be obtained. Our scheme provides a guidance for the construction of a measurement-free, all-optical broadband quantum network utilizing EPR steering swapping.

Experimental sharing of Bell nonlocality with projective measurements

In the standard Bell experiment, two parties perform local projective measurements on a shared pair of entangled qubits to generate nonlocal correlations. However, these measurements completely destroy the entanglement, rendering the post-measurement state unable for subsequent use. For a long time, it was believed that only unsharp measurements can be used to share quantum correlations. Remarkably, recent research has shown that classical randomness assisted projective measurements are sufficient for sharing nonlocality (Steffinlongo and Tavakoli 2022 Phys. Rev. Lett. 129 230402). Here, by stochastically combining no more than two different projective measurement strategies, we report an experimental observation of double Clauser–Horne–Shimony–Holt inequality violations with two measurements in a sequence made on each pair of maximally and partially entangled polarization photons. Our results reveal that the double violation achieved by partially entangled states can be 11 standard deviations larger than that achieved by maximally entangled ones. Our scheme eliminates the requirement for entanglement assistance in previous unsharp-measurement-based sharing schemes, making it experimentally easier. Our work provides possibilities for sharing other types of quantum correlations in various physical systems with projective measurements.

Gravitationally modulated quantum correlations: Discriminating classical and quantum models of ultra-compact objects with Bell nonlocality

We investigate the relation between quantum nonlocality and gravity at the astrophysical scale, both in the classical and quantum regimes. Considering a gedanken experiment involving particle pairs orbiting in the strong gravitational field of ultra-compact objects, we find that the violation of Bell inequality acquires an angular modulation factor that strongly depends on the nature of the gravitational source. We show how such gravitationally-induced modulation of quantum nonlocality readily discriminates between black holes (both classical and inclusive of quantum corrections) and string fuzzballs, i.e., the true quantum description of ultra-compact objects according to string theory. These findings promote Bell nonlocality as a potentially key tool in putting quantum gravity to the test.

Verification of Bell nonlocality by violating quantum monogamy relations

Verification of Bell nonlocality by violating quantum monogamy relations