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

arXiv:1007.1294

Factorization Law for Two Lower Bounds of Concurrence

Sayyed Yahya Mirafzali, Iman Sargolzahi, Ali Ahanj, Kurosh Javidan, Mohsen Sarbishaei

Published Jul 8, 2010• 0 citations
arXivHTMLPDF

Abstract

We study the dynamics of two lower bounds of concurrence in bipartite quantum systems when one party goes through an arbitrary channel. We show that these lower bounds obey the factorization law similar to that of [Konrad et al., Nat. Phys. 4, 99 (2008)]. We also, discuss the application of this property, in an example.
DOI
10.48550/arxiv.1007.1294

Related papers

Factorization law for two lower bounds of concurrence

Sayyed Yahya Mirafzali, Iman Sargolzahi, Ali Ahanj +2 more

We study the dynamics of two lower bounds of concurrence in bipartite quantum systems when one party goes through an arbitrary channel. We show that these lower bounds obey the factorization law similar to that of [Konrad et al., Nat. Phys. 4, 99 (2008)]. We also discuss the application of this property in an example.

Physical Review A•Sep 22, 2010•4 citations

Evolution of entanglement for quantum mixed states

Chang‐shui Yu, X. X. Yi, He‐Shan Song

A simple relation is introduced for concurrence to describe how much the entanglement of a bipartite system is at least left if either (or both) subsystem undergoes an arbitrary physical process. This provides a lower bound for concurrence of mixed states (pure states are included) in contrast to the upper bound given by Konrad et al. [Nat. Phys. 4, 99 (2008)]. Our results are also suitable for general high-dimensional bipartite quantum systems.

arXiv:0812.3959•Physical Review A•Dec 18, 2008•25 citations

Dynamics of the bounds of squared concurrence

Zhao Liu, Heng Fan

The dynamics of the quantum entanglement is a fundamental characteristic for various quantum systems. Since the computable entanglement measure for higher dimensional quantum states itself is absent, the dynamics of the entanglement expressed in an operational method will be of interest. We study the dynamics of $\ensuremath{\tau}$, an analytical lower bound of squared concurrence, of a bipartite $d\ensuremath{\bigotimes}d$ quantum state when one party goes through an arbitrary noisy channel. For a pure input state, the range of $\ensuremath{\tau}$ is obtained explicitly. For a mixed input state, an upper bound of $\ensuremath{\tau}$ is found. Interestingly, the tangle ${\ensuremath{\tau}}^{\ensuremath{'}}$, as an upper bound of squared concurrence, also has a similar dynamical property. Our results are similar to that of Konrad et al. and can help the estimation of high-dimension bipartite entanglement in experiments.

arXiv:0812.2993•Physical Review A•Mar 6, 2009•12 citations

Trace norm related to concurrence

Wei Cheng

By investigating the property of the trace norm which appeared in the analytical lower bound for the concurrence of arbitrary dimensional bipartite quantum states [Phys. Rev. Lett. 95, 040504 (2005)], we demonstrate the limitation of the bound in that paper and provide several concrete examples.

IEEE Congress on Evolutionary Computation (CEC)•Jun 1, 2008•0 citations

Evolution and Symmetry of Multipartite Entanglement

Gilad Gour

We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)10.1038/nphys885]. In addition, for a permutation P, we provide an operational definition of P asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.

arXiv:1008.1292•Physical Review Letters•Nov 5, 2010•44 citations

Lower Bound of Concurrence Based on Generalized Positive Maps

Huihui Qin, Shao-Ming Fei

We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an analytical lower bound of concurrence. Detailed examples are used to show that our bound can detect entanglement better and can improve the well known existing lower bounds.

arXiv:1401.1624•Communications in Theoretical Physics•Dec 1, 2013•2 citations
The dynamics of the quantum entanglement is a fundamental characteristic for various quantum systems. Since the computable entanglement measure for higher dimensional quantum states itself is absent, the dynamics of the entanglement expressed in an operational method will be of interest. We study the dynamics of $\ensuremath{\tau}$, an analytical lower bound of squared concurrence, of a bipartite $d\ensuremath{\bigotimes}d$ quantum state when one party goes through an arbitrary noisy channel. For a pure input state, the range of $\ensuremath{\tau}$ is obtained explicitly. For a mixed input state, an upper bound of $\ensuremath{\tau}$ is found. Interestingly, the tangle ${\ensuremath{\tau}}^{\ensuremath{'}}$, as an upper bound of squared concurrence, also has a similar dynamical property. Our results are similar to that of Konrad et al. and can help the estimation of high-dimension bipartite entanglement in experiments.
We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)10.1038/nphys885]. In addition, for a permutation P, we provide an operational definition of P asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.