Shared purity of multipartite quantum states

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.

Genuine-multipartite-entanglement trends in gapless-to-gapped transitions of quantum spin systems

“…We focus on the N = 16 case, in all the non-integrable models considered in this paper. We calculate the concurrence [54], logarithmic negativity [55], quantum discord [11], and the shared purity [56] for the nearest neighbor density matrices in these models.…”

“…Shared purity [56] is the difference between the "global" and "local" fidelities of an arbitrary (pure or mixed) state ρ. The global fidelity is a measure of the minimum distance of the state ρ from a globally pure state while the local fidelity is a measure of the minimum distance of ρ from a locally pure state.…”

Quantum discord and its allies: a review of recent progress

“…Further examples include Refs. [59,[192][193][194][195][196][197][198][199][200][201][202][203][204][205].…”

Benford's law gives better scaling exponents in phase transitions of quantumXYmodels

“…The scaling exponent found using the Benford magnetization is much higher than many other known scaling exponents for this model. In particular, the scaling exponents for transverse magnetization, fidelity, concurrence, quantum discord, and shared purity (without using the Benford analysis) are significantly lower [7,[15][16][17]. For the transverse magnetization (without using the Benford Note that the procedure for Benford analysis described in this paper is not unique.…”

“…The scaling exponent found using the Benford magnetization is much higher than many other known scaling exponents for this model. In particular, the scaling exponents for transverse magnetization, fidelity, concurrence, quantum discord, and shared purity are significantly lower [7,[15][16][17]. In Fig.…”