Why entanglement of formation is not generally monogamous

摘要

Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if onensystem A is maximally entangled with another system B, it cannot be entangled at all with a third system C. Thisnconcept, known as the monogamy of entanglement, is manifest when the entanglement of A with a pairBC can bendivided as contributions of the entanglement between A and B and A and C, plus a term τABC involving genuinentripartite entanglement and so expected to be always positive. A very important measure in quantum informationntheory, the entanglement of formation (EOF), fails to satisfy this last requirement. Here we present the reasonsnfor that and show a set of conditions that an arbitrary pure tripartite state must satisfy for the EOF to become anmonogamous measure, i.e., for τABC u0002 0. The relation derived is connected to the discrepancy between quantumnand classical correlations, τABC being negative whenever the quantum correlation prevails over the classical one.nThis result is employed to elucidate features of the distribution of entanglement during a dynamical evolution.nIt also helps to relate all monogamous instances of the EOF to the squashed sntanglement, an entanglementnmeasure that is always monogamous.