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Register a new userQuantum nonlocality for entanglement of quasiclassical states
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Entanglement of quasiclassical (coherent) states of two harmonic oscillators leads to striking quantum effects and is useful for quantum technologies. These effects and applications are closely related to nonlocal correlations inherent in these states, manifested by the violation of Bell inequalities. With previous frameworks, this violation is limited by the size of the system, which does not approach the maximum even when the amount of entanglement approaches its maximum. Here we propose a new version of Bell correlation operators, with which a nearly maximal violation can be obtained as long as the associated entanglement approximates to the maximum. Consequently, the revealed nonlocality is significantly stronger than those with previous frameworks for a wide range of the system size. We present a new scheme for realizing the gate necessary for measurement of the nonlocal correlations. In addition to the use in test of quantum nonlocality, this gate is useful for quantum information processing with coherent states
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We have applied an entanglement purification protocol to produce a single entangled pair of photons capable of violating a CHSH Bell inequality from two pairs that individually could not. The initial poorly-entangled photons were created by a controllable decoherence that introduced complex errors. All of the states were reconstructed using quantum state tomography which allowed for a quantitative description of the improvement of the state after purification.
Recently, Halder emph{et al.} [S. Halder emph{et al.}, Phys. Rev. Lett. textbf{122}, 040403 (2019)] present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $2 otimes 2 otimes 2$ quantum system, we show that a set of orthogonal entangled states is locally reducible but locally indistinguishable in all bipartitions, which means the states have strong nonlocality. Furthermore, we generalize the result in N-qubit quantum system, where $Ngeqslant 3$. Finally, we also construct a class of strong nonlocality of entangled states in $dotimes dotimes cdots otimes d, dgeqslant 3$. Our results extend the phenomenon of strong nonlocality for entangled states.
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Bell-type linear inequalities. In contrast to semidefinite programming approaches, our method allows for the consideration of inequalities with abstract weights, by means of leveraging the Hermiticity of quantum states. Recognizing that classical correlations correspond to measurements made on separable states, we also introduce a practical method for obtaining sufficient separability criteria. We specifically vet the candidacy of driven and undriven superradiance as schema for entanglement generation. We conclude by reviewing current approaches to quantum contextuality, emphasizing the operational distinction between nonlocal and contextual quantum statistics. We utilize our abstractly-weighted linear quantum bounds to explicitly demonstrate a set of conditional probability distributions which are simultaneously compatible with quantum contextuality while being incompatible with quantum nonlocality. It is noted that this novel statistical regime implies an experimentally-testable target for the Consistent Histories theory of quantum gravity.
We analyze entanglement and nonlocal properties of the convex set of symmetric $N$-qubits states which are diagonal in the Dicke basis. First, we demonstrate that within this set, positivity of partial transposition (PPT) is necessary and sufficient for separability --- which has also been reported recently in https://doi.org/10.1103/PhysRevA.94.060101 {Phys. Rev. A textbf{94}, 060101(R) (2016)}. Further, we show which states among the entangled DS are nonlocal under two-body Bell inequalities. The diagonal symmetric convex set contains a simple and extended family of states that violate the weak Peres conjecture, being PPT with respect to one partition but violating a Bell inequality in such partition. Our method opens new directions to address entanglement and non-locality on higher dimensional symmetric states, where presently very few results are available.
We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of $mathbb{C}^dotimesmathbb{C}^d$, where $d$ is odd, Zhang emph{et al} have constructed $d^2$ orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. {bf 90}, 022313(2014)]. We find a subset contains with $6d-9$ orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system $mathbb{C}^motimesmathbb{C}^n$. We present a small set with only $3(m+n)-9$ orthogonal product states and prove these states are LOCC indistinguishable. Even though these $3(m+n)-9$ product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.
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