Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit

Abstract

The limitation on the shareability of quantum entanglement over several parties, the so-called monogamy of entanglement, is an issue that has caught considerable attention of quantum informa- tion community over the last decade. A natural question of interest in this connection is whether monogamy of correlations is true for correlations other than entanglement. This issue is examined here by choosing quantum deficit, proposed by Rajagopal and Rendell, an operational measure of correlations. In addition to establishing the polygamous nature of the class of three qubit sym- metric pure states characterized by two distinct Majorana spinors (to which the W states belong), those with three distinct Majorana spinors (to which GHZ states belong) are shown to either obey or violate monogamy relations. While the generalized W states can be mono/polygamous, the generalized GHZ states exhibit monogamy with respect to quantum deficit. The issue of us- ing monogamy conditions based on quantum deficit to witness the states belonging to SLOCC inequivalent classes is discussed in the light of these results.

15 pages, 2 figures, 1 table

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• Nonlocality and Entanglement for Symmetric States
• Monogamy deficit for quantum correlation in multipartite quantum system
• Multipartite quantum correlations in even and odd spin coherent states
• Monogamy of entanglement for tripartite systems
• Universal quantum correlation close to quantum critical phenomena
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• Shared Purity of Multipartite Quantum States
• Spin squeezing in symmetric multiqubit states with two distinct Majorana spinors
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• Quantum discord in photon added Glauber coherent states of $\mathrm{GHZ}$-type
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