A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schrödinger cat states

Abstract

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of k qubits is presented. We especially focus on the reduced states of k qubits obtained from a balanced superposition of symmetric n-qubit states (multiqubit Schrödinger cat states) by tracing out n − k particles (k = 2, 3, . . . , n−1). Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the parity grouping (k − 1) qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising k, k −1, . . . and two particles. A detailed analysis is given for two-, three-and four-qubit systems. In the second scheme, the subsystem comprising the (k − 1) qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multiqubits systems. The explicit expressions of classical states presenting zero discord are derived.

Dynamics of quantum correlations in a qubit-qutrit spin system under random telegraph noise

“…The first measure of quantumness of correlations generally more than entanglement is quantum discord (QD) [21][22][23][24] that has faced a great deal of attention [25,26]. The QD allows one to reach all the non-classical correlations even beyond the entanglement, which may exist for mixed separable quantum states [27]. There are some difficulties in operational quantum tasks involved with the QD that come from the problematic solution of the QD through a minimization procedure [28][29][30].…”

Hilbert–Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

“…x t = (0, 0, T 300 ) (47) and the 3 × 15 matrix given by T = (T iαβ ) with i = 1, 2, 3 (α, β) = (0, 0).…”

“…The generalized X states are of paramount importance in investigating quantum correlations for a collection of spin-1/2 particles possessing discrete symmetries like particle exchange symmetry and/or parity invaraince. For instance, the reduced density matrices of multipartite Schrödinger cat states, which are invariant under permutation symmetry, are X structured operators (see for instance the reference [47]). Completely symmetric systems, including Dicke states, are relevant in many experimental situations such as spin squeezing which may have potential applications in atomic interferometers and high atomic clocks (see [48] and references therein) .…”