arXiv:quant-ph/0502176 · Physical Review Letters

General Monogamy Inequality for Bipartite Qubit Entanglement

Tobias J. Osborne, Frank Verstraete

Published Jun 7, 2006• 732 citations

Abstract

We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy inequality to the concept of frustration of correlations in quantum spin systems.

DOI: 10.1103/physrevlett.96.220503

Related papers

Violation of monogamy inequality for qutrits and higher dimensional objects

Yong Cheng Ou

Bipartite quantum entanglement for qutrits or higher dimensional objects is considered. In a not strict sense but with an explicit two-qutrit antisymmetric state example, it is proved that a monogamy inequality for qubits introduced by Coffman, Kundu, and Wootters may be violated for their entanglement quantified by the concurrence in qutrits or higher dimensional objects.

Dec 15, 20060 citations

Strong Monogamy Conjecture for Multiqubit Entanglement: The Four-Qubit Case

Bartosz Regula, Sara Di Martino, Soojoon Lee +1 more

We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular, we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.

arXiv:1405.3989Physical Review LettersSep 10, 201493 citations

Strong monogamy of four-qubit entanglement

Bartosz Regula, Sara Di Martino, Soojoon Lee +1 more

We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.

May 15, 20140 citations

Strong monogamy inequalities for four qubits

Bartosz Regula, Andreas Osterloh, Gerardo Adesso

We investigate possible generalizations of the Coffman-Kundu-Wootters monogamy inequality to four qubits, accounting for multipartite entanglement in addition to the bipartite terms. We show that the most natural extension of the inequality does not hold in general, and we describe the violations of this inequality in detail. We investigate alternative ways to extend the monogamy inequality to express a constraint on entanglement sharing valid for all four-qubit states, and perform an extensive numerical analysis of randomly generated four-qubit states to explore the properties of such extensions.

arXiv:1604.03419Physical Review AMay 31, 201632 citations

Proper monogamy inequality for arbitrary pure quantum states

Yong-Cheng Ou, Heng Fan, Shao-Ming Fei

We provide a detailed proof of an analytical lower bound of entanglement quantified by concurrence for arbitrary bipartite quantum states. It is shown that though the bound does not allow one to detect bound entanglement, it is tight for some mixed states and can detect most of the free entanglement. On the other hand, it is known that the entanglement monogamy inequality proposed by Coffman, Kundu, and Wootters is, in general, not true for higher-dimensional quantum states. Inducing from the lower bound of concurrence, we find a proper form of entanglement monogamy inequality for arbitrary pure quantum states.

arXiv:0711.2865Physical Review AJul 9, 200882 citations

Investigation of Momogamy Relations and Their Inequalities in Multipartite Quantum Systems

Zahra Feizi Chanaghblaghi

As the quantum entangled states are as a source for many of branches different quantum information theory, such as dense encoding,encryption and teleportation, theoretical study of any relation between the different parts of a entangled quantum state of semi-transparent. One of these relations, inequality monogamy. Although the correlation classical can be freely in the multipartite systems will be shared, the famous that quantum entanglement in this share has restrictions. This restriction on the sharing of entanglement, the famous to monogamy in the multipartite quantum systems. In terms of math, monogamy in the entanglement the first was introduced by Coffman-Kundu-Wootters (CKW) in the three qubit systems. Inequality CKW that obtained for the measure concurrence, mutually unique nature of entanglement two qubits common in the three qubit systems shows. A simple example of the monogamy property can be expressed that the amount of entanglement between A and B to add the amount of entanglement between A and C cannot be greater than the amount of entanglement between A and pair BC. The aim of this thesis reviews the types monogamy inequality defined for the various entangled measures especially measure concurrence.

Jan 1, 20170 citations