Concurrence

About: Concurrence is a research topic. Over the lifetime, 866 publications have been published within this topic receiving 15389 citations.

Scaling of Entanglement close to a Quantum Phase Transitions

Abstract: In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.

Universal state inversion and concurrence in arbitrary dimensions

Abstract: Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters's concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT Superoperator.

Four qubits can be entangled in nine different ways

Abstract: We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.

Entanglement of formation and concurrence

Abstract: Entanglement of formation is one of three widely studied measures of entanglement of a general bipartite system This paper reviews our current understanding of entanglement of formation and the related concept of concurrence, including discussions of additivity, the problem of finding explicit formulas, and connections between concurrence and other properties of bipartite states

General monogamy inequality for bipartite qubit entanglement.

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