Shared purity of multipartite quantum states
Anindya Biswas, Aditi Sen, Ujjwal Sen · Physical Review A · 2014
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 although it detects a quantum feature of the shared state, it is different from quantum correlations. 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 Greenberger-Horne-Zeilinger states are monogamous, while all generalized W states are nonmonogamous with respect to this measure. We apply the quantity to investigate the quantum XY spin-1/2 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.