Shared Purity of Multipartite Quantum States

TL;DR

This paper introduces shared purity, a new measure for quantum states that captures quantum correlations and can detect quantum phase transitions in spin models, with distinct monogamy properties for different entangled states.

Contribution

It defines shared purity for multipartite quantum states, proves its quantum nature and monogamy properties, and demonstrates its effectiveness in detecting quantum phase transitions.

Findings

Shared purity is different from quantum correlations.

Generalized GHZ states are monogamous with respect to shared purity.

Shared purity detects quantum phase transitions in XY spin models.

Abstract

Fidelity plays an important role in measuring distances between pairs of quantum states, of single as well as multiparty systems. Based on the concept of fidelity, we introduce a physical quantity, shared purity, for arbitrary pure or mixed quantum states of shared systems of an arbitrary number of parties in arbitrary dimensions. We find that it is different from quantum correlations. However, we prove that a maximal shared purity between two parties excludes any shared purity of these parties with a third party, thus ensuring its quantum nature. Moreover, we show that all generalized GHZ states are monogamous, while all generalized W states are non-monogamous with respect to this measure. We apply the quantity to investigate the quantum XY spin models, and observe that it can faithfully detect the quantum phase transition present in these models. We perform a finite-size scaling analysis and find the scaling exponent for this quantity.