Quantum Discord in Photon-Added Glauber Coherent States of GHZ-Type

Abstract

We investigate the influence of photon excitations on quantum correlations in tripartite Glauber coherent states of Greenberger-Horne-Zeilinger type. The pairwise correlations are measured by means of the entropy-based quantum discord. We also analyze the monogamy property of quantum discord in this class of tripartite states in terms of the strength of Glauber coherent states and the photon excitation order. 1In the context of information processing and transmission, several theoretical and experimental results confirm the advantages of quantum protocols compared to their classical counterparts (see for instance [1,2,3]). Quantum technology exploiting the intriguing phenomena of quantum world, such as entanglement, offers secure ways for communication [4,5] and potentially powerful algorithms in quantum computation [6]. Originally, quantum information processing focused on discrete (finitedimensional) entangled states like the polarizations of a photon or discrete levels of an atom. But, the extension from discrete to continuous variables has been also proven beneficial in coding and manipulating efficiently quantum information. Coherent states, which constitute the prototypical instance of continuous-variables states, are expected to play a central role in this context. They are appealing for their mathematical elegance (continuity and over-completion property) and closeness to classical physical states (minimization of Heisenberg uncertainty relation). Implementing a logical qubit encoding by treating entangled coherent states as qubits in a two dimensional Hilbert space has been shown a promising strategy in performing successfully various quantum tasks such as quantum teleportation [7,8], quantum computation [9, 10, 11], entanglement purification [12] and errors correction [13]. In view of these potential applications, a special attention was paid, during the last years, to the identification, characterization and quantification of quantum correlations in bipartite coherent states systems (see for instance the papers [14,15,16] and references therein). The bipartite treatment was extended to superpositions of multimode coherent states [17,18,19,20,21] which exhibit multipartite entanglement. One may quote for instance entanglement properties in GHZ (Greenberger-Horne-Zeilinger), W (Werner) states discussed in [22,23] and entangled coherent state extensions of cluster qubits investigated in [24,25,26]. To quantify quantum correlations beyond entanglement in coherent states systems, measures such as quantum discord [27,28] and its geometric variant [29] were used.Explicit results were derived for quantum discord [30,31,32,33,34,35,36,37] and geometric quantum discord [38,39,40,41] for some special sets of coherent states.On the other hand, decoherence is a crucial process to understand the emergence of classicality in quantum systems. It describes the inevitable degradation of quantum correlations due to experimental and environmental noise. Various decoherence models were investigated and in particular the ph...

Local quantum uncertainty and Non-commutativity measure discord in two-mode photon-added entangled coherent states

“…In recent years, there has been a focus on the identification, characterization, and quantification of quantum correlations in systems with bipartite coherent states as well as multimode coherent states [42][43][44][45]. In this sense, a class of photon-added Bell-type entangled coherent states (PABECSs) were introduced and studied in [46][47][48][49]. PABECSs were obtained from Bell type entangled coherent states by applying creation operators.…”