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Modern Physics Letters B

Distribution of geometric quantum discord in photon-added coherent states

Mohammed Daoud A, W. Kaydi, Hanane El Hadfi

Published Dec 30, 2015• 3 citations
Publisher

Abstract

In this paper, we examine the influence of photon excitation on the monogamy property of quantum discord in tripartite coherent states of Greenberger–Horne–Zeilinger (GHZ) type. The Hilbert–Schmidt norm is used as quantifier of pairwise quantum correlations. The geometric quantum discord in all bipartite subsystems are explicitly given. We show that the geometric discord is monogamous for any photon excitation order.

DOI
10.1142/s0217984915502395

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Modern Physics Letters B•Feb 28, 2013•5 citations
In this paper, we examine the influence of photon excitation on the monogamy property of quantum discord in tripartite coherent states of Greenberger–Horne–Zeilinger (GHZ) type. The Hilbert–Schmidt norm is used as quantifier of pairwise quantum correlations. The geometric quantum discord in all bipartite subsystems are explicitly given. We show that the geometric discord is monogamous for any photon excitation order.
We introduce a monogamy inequality for quantum correlations, which implies that the sum of pairwise quantum correlations is upper limited by the amount of multipartite quantum correlations as measured by the global quantum discord. This monogamy bound holds either for pure or mixed quantum states provided that bipartite quantum discord does not increase under discard of subsystems. We illustrate the monogamy behavior for multipartite pure states with Schmidt decomposition as well as for WWW-GHZ mixed states. As a by-product, we apply the monogamy bound to investigate residual multipartite correlations.
A model of dynamics of quantum correlations of two modes quasi-Bell cat states, based on Glauber coherent states, is considered. The analytic expressions of pairwise entanglement of formation, quantum discord and its geometrized variant are explicitly derived. We analyze the distribution of quantum correlations between the two modes and the environment. We show that, in contrast with squared concurrence, entanglement of formation, quantum discord and geometric quantum discord do not follow the property of monogamy except in some particular situations that we discuss.
Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.
In this paper, we obtain the pairwise quantum discord for a three-qubit W-class state, and investigate the monogamy property of quantum discord by two different ways (relative entropy-based distance and geometric square-norm distance). Through numerical calculations, we find that a party cannot have maximal quantum correlations with the other two parties simultaneously. For the given state, the quantum correlation between particles 1 and 3 induces limitation on the quantum correlation between them and particle 2. Moreover, the result also shows that the geometric quantum discord of the given W-class state obeys the monogamy property while the entropy quantum discord violates.