2017/04/30 by A. P. Majtey, D. Bussandri, Diego G. Bussandri +6 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Basis (linear algebra) #Commutative property #Computer science #Discrete mathematics #Estimator #Mathematics #Measure (data warehouse) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum state #Qubit #Representation (politics) #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.1007/s11128-017-1669-9
published in Quantum Information Processing 16(9) (Springer Science+Business Media) · 6 pages, 4 figures
openalex publication_date 2017/07/28 · arxiv created 2017/08/24 · arxiv updated 2017/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work we analyze a non-commutativity measure of quantum correlations recently proposed by Y. Guo [Sci. Rep. 6, 25241 (2016)]. By recourse to a systematic survey of a two-qubit system, we detected an undesirable behavior of such a measure related to its representation-dependence. In the case of pure states, this dependence manifests as a non-satisfactory entanglement measure whenever a representation other than the Schmidt's is used. In order to avoid this dependence on the basis, we argue that a minimization procedure over the set of all possible representations of the quantum state is required. In the case of pure states, this minimization can be analytically performed and the optimal basis turns out to be that of Schmidt's. In addition, the resulting measure inherits the main properties of Guo's measure and, unlike the latter, it reduces to a legitimate entanglement measure in the case of pure states. Some examples involving general mixed states are also analyzed considering such a optimization. The results show that, in most cases of interest, the use of Guo's measure can result in a overestimation of quantum correlations. However, since Guo's measure has the advantage of being easily computable, it might be used as a qualitative estimator of the presence of quantum correlations.