A monogamy equalities of complementarity relation and distribute entanglement for multi-qubit pure states

TL;DR

This paper establishes new monogamy relations and complementarity inequalities for quantum correlations in multi-qubit pure states, providing a deeper understanding of entanglement distribution and quantum correlations.

Contribution

It introduces a novel method to detect genuine quantum correlations and derives new monogamy laws and equalities for multi-qubit systems, extending previous results.

Findings

Existence of strict monogamy laws for quantum correlations in multi-qubit systems

Derivation of a proper form of entanglement monogamy equality for arbitrary states

Characterization of quantum correlation of a qubit with the rest of the system

Abstract

We propose a method to detect genuine quantum correlation for multi-qubit pure states. We then derive a complementarity relations for pure quantum states of N qubits. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. On the other hand, it is known that the entanglement monogamy equality proposed by Coffman, Kundu, and Wootters is in general not true for multiqubit states. Inducing from the CKW equality, we find a proper form of entanglement monogamy equality for arbitrary quantum states. The total quantum correlation of qubit k with the remaining qubits Rk can be characterizes. Furthermore, the quantum correlation of qubit mn with the remaining qubits Rmn can also be obtained. Furthermore, some monogamy relations have been obtained.