A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states

TL;DR

This paper introduces a recursive method to compute geometric quantum discord in symmetric multiqubit Schr"odinger cat states, providing explicit formulas and analyzing different bipartition schemes.

Contribution

It presents a novel recursive approach to quantify quantum correlations in symmetric multiqubit states, unifying different bipartition schemes and deriving explicit formulas.

Findings

Explicit recursive formulas for quantum discord in multiqubit states.

Equivalence of two bipartition schemes in measuring correlations.

Derived classical states with zero discord.

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 Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ 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 multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.