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Journal of the Korean Physical Society

Super quantum discord and other correlations for tripartite GHZ-type squeezed states

Saad Rfifi, Fatima-Zahra Siyouri, M. El Baz, Y. Hassouni

Published Jul 1, 2015• 4 citations
Publisher

Abstract

A comparison is made between normal discord, super quantum discord, and entanglement for the tripartite Greenberger-Horne-Zeilinger (GHZ)-type squeezed states. For this aim, we start by studying the behavior of quantum discord for tripartite GHZ-type squeezed states. Also, we verify the monotonicity of the super quantum discord according to weaker quantum measurements. This was done by manipulating the amount of quantum information lost during the disruption of our quantum system and by controlling the measurement strength. Furthermore, we calculate the entanglement for our system.

DOI
10.3938/jkps.67.311

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A comparison is made between normal discord, super quantum discord, and entanglement for the tripartite Greenberger-Horne-Zeilinger (GHZ)-type squeezed states. For this aim, we start by studying the behavior of quantum discord for tripartite GHZ-type squeezed states. Also, we verify the monotonicity of the super quantum discord according to weaker quantum measurements. This was done by manipulating the amount of quantum information lost during the disruption of our quantum system and by controlling the measurement strength. Furthermore, we calculate the entanglement for our system.
Quantum discord is a measure of nonclassical correlations in quantum systems. While the bipartite version of quantum discord is experimentally well-studied, the multipartite version has never been convincingly measured. In this study, we experimentally investigate tripartite quantum discord using an NMR quantum information processor. Building on a theoretical framework for conditional projective measurements and quantum conditional mutual information, we quantify the tripartite quantum discord and its contributions in different three-qubit states such as the Greenberger-Horne-Zeilinger (GHZ) and Werner (W) states as well as classical mixtures of biseparable Bell states, and classical mixtures of product states. The experiments employed full quantum state tomography and temporal averaging to prepare mixed states, achieving fidelities exceeding 95%. Our results confirm that quantum discord persists even in the absence of entanglement, highlighting its utility as a broader indicator of quantum correlations. Furthermore, we validate the nonconvexity of discord, confirming that classical mixtures of zero-discord states can exhibit nonzero discord. This experimentally confirms that quantum discord does not fit into the framework of resource theory. This work establishes a robust methodology for measuring quantum discord, illuminating the structure and distribution of quantum correlations in multipartite systems.
A new measure based on the tripartite information diagram is proposed for identifying quantum discord in tripartite systems. The proposed measure generalizes the mutual information underlying discord from bipartite to tripartite systems, and utilizes both one-particle and two-particle projective measurements to reveal the characteristics of the tripartite quantum discord. The feasibility of the proposed measure is demonstrated by evaluating the tripartite quantum discord for systems with states close to Greenberger–Horne–Zeilinger, W, and biseparable states. In addition, the connections between tripartite quantum discord and two other quantum correlations—namely genuine tripartite entanglement and genuine tripartite Einstein–Podolsky–Rosen steering—are briefly discussed. The present study considers the case of quantum discord in tripartite systems. However, the proposed framework can be readily extended to general N-partite systems.
Abstract In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner function for mixed tripartite squeezed states of Greenberger–Horne–Zeilinger (GHZ) type then we compare their behaviors. We show that the role of Wigner function in detecting and quantifying bipartite quantum correlation [Int. J. Mod. Phys. B 30 (2016) 1650187] may be generalized to the multipartite case.
We calculate the analytic expression for geometric measure of entanglement for arbitrary superposition of two NNN-qubit canonical orthonormal Greenberger-Horne-Zeilinger (GHZ) states and the same for two WWW states. In the course of characterizing all kinds of nonclassical correlations, an explicit formula for quantum discord (via relative entropy) for the former class of states has been presented. Contrary to the GHZ state, the closest separable state to the WWW state is not classical. Therefore, in this case, the discord is different from the relative entropy of entanglement. We conjecture that the discord for the NNN-qubit WWW state is log2N\mathrm{log}{}_{2}Nlog2​N.
In this work, the quantum discord and tripartite entanglement in the presence of an asymptotically flat static black hole are discussed. The total correlation, quantum discord, and classical correlation are found to exhibit decreasing behavior with increasing Hawking temperature. It is shown that the classical correlation is less than the quantum discord in the full range of Hawking temperature. The tripartite entanglements for Greenberger–Horne–Zeilinger (GHZ) and W-states also exhibit decreasing behavior with increasing Hawking temperature. When the Hawking temperature approaches the infinite limit, the tripartite entanglements of the GHZ and W-states reduce, in terms of the π-tangle, to 52% and 33% of the corresponding values in the flat space limit, respectively.