Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

A Simplified and Obvious Expression of Concurrence in Wootters‘ Measure of Entanglement of a Pair of Qubits

王安民

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

We obtain a simplified and obvious expression of“concurrence” in Wootters' measure of entanglement of a pair of qubits that have no more than two non-zero eigenvalues in terms of the concurrences of eigenstates and theirsimple combinations. It not only simplifies the calculation of Wootters' measure of entanglement, but also revealssome general and important features. Our conclusions are helpful for the further understanding and applicationof quantum entanglement.

Related papers

A Simplified and Obvious Expression of Concurrence in Wootters' Measure of Entanglement of a Pair of Qubits

Wang An-Min

We obtain a simplified and obvious expression of ``concurrence" in Wootters' measure of entanglement of a pair of qubits that have no more than two non-zero eigenvalues in terms of the concurrences of eigenstates and their simple combinations. It not only simplifies the calculation of Wootters' measure of entanglement, but also reveals some general and important features. Our conclusions are helpful for the further understanding and application of quantum entanglement.

arXiv:quant-ph/0208036•Chinese Physics Letters•Nov 1, 2003•19 citations

Measurable entanglement

Alexander A. Klyachko, Barış Öztop, A.S. Shumovsky

The amount of entanglement carried by a quantum bipartite state is usually evaluated in terms of concurrence [S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997); P. Rungta, V. Bužek, C. M. Caves, M. Hillery, and G. J. Milburn, Phys. Rev. A 64, 042315 (2001)]. We give a physical interpretation of concurrence that reveals a way of its direct measurement and discuss possible generalizations.

arXiv:quant-ph/0512197•Applied Physics Letters•Mar 20, 2006•28 citations

Generalized entanglement measure for continuous-variable systems

S. Nibedita Swain, Vineeth S. Bhaskara, Prasanta Kumar Panigrahi

Concurrence, introduced by Hill and Wootters [Hill and Wootters, Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of the entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Bhaskara and Panigrahi, Quantum Inf. Process. 16, 118 (2017)] for pure discrete-variable systems in arbitrary dimensions and extending the concept to mixed continuous-variable states. A family of faithful entanglement measures is constructed that admits necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Vedral, Plenio, Rippin, and Knight, Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states, and non-Gaussian continuous-variable Bell states matches with known results. We also quantify entanglement of phase-randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.

arXiv:1706.01448•Physical Review A•May 27, 2022•11 citations

Concurrence of the mixed state of two non-orthogonal pure states

Di Yao-Min, Baolin Hu, Liu Dong-Dong +2 more

In this article an obvious expression of concurrence of the mixed state of two non-orthogonal pure states in two qubits is derived. The result reveals that the expression of concurrence of the mixed state of two orthogonal states can be directly generalized to the case of the mixed state of two non-orthogonal states. Then the maximally entangled states mixed by two pure states and the concurrences in some important special cases are discussed.

Acta Physica Sinica•Jan 1, 2006•7 citations

Typical entanglement in multiple-qubit systems

Viv M. Kendon, Kae Nemoto, William J. Munro

Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood; however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter concurrence formula) as N increases. Above six qubits, very few states have any pairwise entanglement and, generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become positive partial transpose (i.e. separable or only bound entangled) around N ⪆ 2m + 3, based on numerical analysis up to N = 13.

arXiv:quant-ph/0106023•Journal of Modern Optics•Aug 1, 2002•42 citations

Estimating Entanglement Monotones with a Generalization of the Wootters Formula

Zhihua Chen, Zhihao Ma, Otfried Gühne +1 more

Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite systems. We demonstrate that for certain families of states our results constitute the strongest bipartite entanglement criterion so far; moreover, they allow us to recognize novel families of multiparticle bound entangled states.

arXiv:1207.2889•Physical Review Letters•Nov 16, 2012•50 citations
We obtain a simplified and obvious expression of“concurrence” in Wootters' measure of entanglement of a pair of qubits that have no more than two non-zero eigenvalues in terms of the concurrences of eigenstates and theirsimple combinations. It not only simplifies the calculation of Wootters' measure of entanglement, but also revealssome general and important features. Our conclusions are helpful for the further understanding and applicationof quantum entanglement.
Concurrence, introduced by Hill and Wootters [Hill and Wootters, Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is strictly positive for entangled states and vanishes for all separable states. We present an extension of the entanglement measure to general pure continuous variable states of multiple degrees of freedom by generalizing the Lagrange's identity and wedge product framework proposed by Bhaskara and Panigrahi [Bhaskara and Panigrahi, Quantum Inf. Process. 16, 118 (2017)] for pure discrete-variable systems in arbitrary dimensions and extending the concept to mixed continuous-variable states. A family of faithful entanglement measures is constructed that admits necessary and sufficient conditions for separability across arbitrary bipartitions presented by Vedral et al. [Vedral, Plenio, Rippin, and Knight, Phys. Rev. Lett. 78, 2275 (1997)]. The computed entanglement measure in the present approach for general Gaussian states, pair-coherent states, and non-Gaussian continuous-variable Bell states matches with known results. We also quantify entanglement of phase-randomized squeezed states and superposition of squeezed states. Our results also simplify several results in quantum entanglement theory.
Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood; however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter concurrence formula) as N increases. Above six qubits, very few states have any pairwise entanglement and, generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become positive partial transpose (i.e. separable or only bound entangled) around N ⪆ 2m + 3, based on numerical analysis up to N = 13.
Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite systems. We demonstrate that for certain families of states our results constitute the strongest bipartite entanglement criterion so far; moreover, they allow us to recognize novel families of multiparticle bound entangled states.