98,307 research outputs found
Monogamy of entanglement without inequalities
We provide a fine-grained definition for monogamous measure of entanglement
that does not invoke any particular monogamy relation. Our definition is given
in terms an equality, as oppose to inequality, that we call the "disentangling
condition". We relate our definition to the more traditional one, by showing
that it generates standard monogamy relations. We then show that all quantum
Markov states satisfy the disentangling condition for any entanglement
monotone. In addition, we demonstrate that entanglement monotones that are
given in terms of a convex roof extension are monogamous if they are monogamous
on pure states, and show that for any quantum state that satisfies the
disentangling condition, its entanglement of formation equals the entanglement
of assistance. We characterize all bipartite mixed states with this property,
and use it to show that the G-concurrence is monogamous. In the case of two
qubits, we show that the equality between entanglement of formation and
assistance holds if and only if the state is a rank 2 bipartite state that can
be expressed as the marginal of a pure 3-qubit state in the W class.Comment: 9 pages + 14 Pages appendix, Final Version, Accepted by Quantu
- …