Monogamy equality in $2\otimes 2\otimes d$ quantum systems

Abstract

There is an interesting property about multipartite entanglement, called the monogamy of entanglement. The property can be shown by the monogamy inequality, called the Coffman-Kundu-Wootters inequality [Phys. Rev. A {\bf 61}, 052306 (2000); Phys. Rev. Lett. {\bf 96}, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance, ${\mathcal{C}}_{A(BC)}^2={\mathcal{C}}_{AB}^2+({\mathcal{C}}_{AC}^a{)}^2$, in the three-qubit system. In this paper, we consider the monogamy equality in $2\otimes 2\otimes d$ quantum systems. We show that ${\mathcal{C}}_{A(BC)}={\mathcal{C}}_{AB}$ if and only if ${\mathcal{C}}_{AC}^a=0$, and also show that if ${\mathcal{C}}_{A(BC)}={\mathcal{C}}_{AC}^a$ then ${\mathcal{C}}_{AB}=0$, while there exists a state in a $2\otimes 2\otimes d$ system such that ${\mathcal{C}}_{AB}=0$ but ${\mathcal{C}}_{A(BC)}>{\mathcal{C}}_{AC}^a$.

4 pages, no figure

References in corpus (8)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Distributed Entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Separability and entanglement of composite quantum systems
• Duality for monogamy of entanglement
• Deterministic Entanglement of Assistance and Monogamy Constraints
• Measurable entanglement for tripartite quantum pure states of qubits
• Entanglement of three-qubit pure states in terms of teleportation capability

Cited by in corpus (6)

• Entanglement monogamy and entanglement evolution in multipartite systems
• Polygamy of Distributed Entanglement
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Concurrence of assistance and Mermin inequality on three-qubit pure states
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Monogamous nature of symmetric multiqubt states with distinct spinors