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arXiv:1612.02524 · Physics Letters A

Complementarity and nonlocality in two-qudit systems

Hai Wang, Asutosh Kumar, Junde Wu

Published Jan 4, 2018• 0 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2017.12.053

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Qubits exhibit extreme nonlocality when their state is maximally entangled and this is observed by mutually unbiased local measurements. This criterion does not hold for the Bell inequalities of high-dimensional systems (qudits), recently proposed by Collins–Gisin–Linden–Massar–Popescu and Son–Lee–Kim. Taking an alternative approach, called the quantum-to-classical approach, we derive a series of Bell inequalities for qudits that satisfy the criterion as for the qubits. In the derivation each d -dimensional subsystem is assumed to be measured by one of d possible measurements with d being a prime integer. By applying to two qubits ( d =2), we find that a derived inequality is reduced to the Clauser–Horne–Shimony–Holt inequality when the degree of nonlocality is optimized over all the possible states and local observables. Further applying to two and three qutrits ( d =3), we find Bell inequalities that are violated for the three-dimensionally entangled states but are not violated by any two-dimensionally entangled states. In other words, the inequalities discriminate three-dimensional (3D) entanglement from two-dimensional (2D) entanglement and in this sense they are genuinely 3D. In addition, for the two qutrits we give a quantitative description of the relations among the three degrees of complementarity, entanglement and nonlocality. It is shown that the degree of complementarity jumps abruptly to very close to its maximum as nonlocality starts appearing. These characteristics imply that complementarity plays a more significant role in the present inequality compared with the previously proposed inequality.
We report on some quantum properties of physical systems, namely, entanglement, nonlocality, k-copy nonlocality (superactivation of nonlocality), hidden nonlocality (activation of nonlocality through local filtering) and the activation of nonlocality through tensoring and local filtering. The aim of this work is two-fold. First, we provide a review of the numerical procedures that must be followed in order to calculate the aforementioned properties, in particular, for any two-qubit system, and reproduce the bounds for two-qudit Werner states. Second, we use such numerical tools to calculate new bounds of these properties for two-qudit Isotropic states and two-qubit Hirsch states.