Abstract
Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if one system is maximally entangled with another system , it cannot be entangled at all with a third system . This concept, known as the monogamy of entanglement, is manifest when the entanglement of with a pair can be divided as contributions of the entanglement between and and and , plus a term 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 . The relation derived is connected to the discrepancy between quantum and classical correlations, 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.
- Received 7 November 2012
DOI:https://doi.org/10.1103/PhysRevA.87.032317
©2013 American Physical Society