2011/10/31 by F. F. Fanchini, M. C. de Oliveira, L. K. Castelano +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Mathematics #Measure (data warehouse) #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum correlation #Quantum discord #Quantum entanglement #Quantum mechanics #Squashed entanglement #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.87.032317
published as Phys. Rev. A 87, 032317 (2013) · 7 pages, 3 figures. Extended version
arxiv created 2012/01/25 · openalex publication_date 2013/03/13 · arxiv updated 2013/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if one system A is maximally entangled with another system B, it cannot be entangled at all with a third system C. This concept, known as the monogamy of entanglement, is manifest when the entanglement of A with a pair BC can be divided as contributions of the entanglement between A and B and A and C, plus a term \ensuremathτABC involving genuine tripartite entanglement and so expected to be always positive. A very important measure in quantum information theory, the entanglement of formation (EOF), fails to satisfy this last requirement. Here we present the reasons for that and show a set of conditions that an arbitrary pure tripartite state must satisfy for the EOF to become a monogamous measure, i.e., for \ensuremathτABC\ensuremath≥0. The relation derived is connected to the discrepancy between quantum and classical correlations, \ensuremathτABC being negative whenever the quantum correlation prevails over the classical one. This result is employed to elucidate features of the distribution of entanglement during a dynamical evolution. It also helps to relate all monogamous instances of the EOF to the squashed sntanglement, an entanglement measure that is always monogamous.