Squashed entanglement and entanglement of purification are quantum mechanical
correlation measures and defined as certain minimisations of entropic
quantities. We present the first non-trivial calculations of both quantities.
Our results lead to the conclusion that both measures can drop by an arbitrary
amount when only a single qubit of a local system is lost. This property is
known as "locking" and has previously been observed for other correlation
measures, such as the accessible information, entanglement cost and the
logarithmic negativity.
In the case of squashed entanglement, the results are obtained with the help
of an inequality that can be understood as a quantum channel analogue of
well-known entropic uncertainty relations. This inequality may prove a useful
tool in quantum information theory.
The regularised entanglement of purification is known to equal the
entanglement needed to prepare a many copies of quantum state by local
operations and a sublinear amount of communication. Here, monogamy of quantum
entanglement (i.e., the impossibility of a system being maximally entangled
with two others at the same time) leads to an exact calculation for all quantum
states that are supported either on the symmetric or on the antisymmetric
subspace of a dxd-dimensional system.Comment: 7 pages revtex4, no figures. v2 has improved presentation and a
couple of references adde