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

TL;DR

This paper investigates the monogamy properties of quantum correlations, specifically quantum deficit, in three-qubit pure states, revealing different behaviors for W and GHZ states and exploring implications for classifying quantum states.

Contribution

It introduces the analysis of quantum deficit monogamy in three-qubit states, highlighting differences between W and GHZ states and their classification implications.

Findings

W states can be mono/polygamous with respect to quantum deficit.

GHZ states obey monogamy of quantum deficit.

Quantum deficit monogamy can distinguish SLOCC classes.

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.