Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, given a quantum state, it is not a simple question to identify whether it is entangled or not. We study the entanglement of quantum systems in arbitrary dimensions using the Bloch representation of density matrix. This approach enables us to consider quantum entanglement geometrically. We first analyze the effect of local Bloch vector on determining whether a quantum state is entangled or separable, and obtain an entanglement criterion related to local Bloch vector, which is stronger than the criterion that only considers the correlation matrix. This criterion is equivalent to the optimized computable cross norm criterion in [14]. Our proof is considered from the perspective of Bloch representation, and there is no need to know the matrix relignment in advance. This criterion also be extended to the problem of the separability of tripartite quantum states. We then combine the local filtering transformation with this entanglement criterion. After applying a suitable local filtering transformation, the quantum state has at most one nonzero Bloch vector, and examples are given to illustrate that the local filtering transformation can help detect some bound states where the original entanglement criterion fails. Moreover, for a finite-dimensional quantum system in which one party is a qubit, we give an analytical form of the combined entanglement criterion.

International Conference on Big Data Computing and Communications (BigCom)Aug 1, 20210 citations

Optimal local filtering operation for enhancing quantum entanglement

Zhaofeng Su, Nina Sukhodoeva

Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. Thus, distilling more entanglement from less entangled resource is a task of practical significance and has been investigated for decades. The literature [Verstraete \textit{et al}., \href{https://link.aps.org/doi/10.1103/PhysRevA.64.010101}{Phys. Rev. A 64, 010101(2001)}] considered a scenario to increase the entanglement by local filtering operation and qualitatively derived the variance relation of entanglement. We investigate the scenario with general two-qubit resources to find the optimal strategy of filtering operations. We obtain the upper bound for the ratio of entanglement increase and find the corresponding optimal local filtering operation to achieve the maximal ratio. Our analysis shows that the upper bound ratio grows with the length of local Bloch vector while the success probability decrease with it. We further extend the research to investigate the optimal measurement strategy by considering general measurement. Our result shows that local measurement can not increase the expectation of quantum entanglement, which gives more analytical evidence to the well known fact that local operation can not create quantum entanglement.

arXiv:2401.08944Jan 17, 20240 citations