Entanglement conditions and entanglement measures

This project explores bounds on entanglement negativity using operator inequalities,

building on the results of [1].

We are looking for a way to quantify entanglement, as an alternative to calculating

the full negativity, which would otherwise require the computation of the

partial transpose of the reduced density matrix, a laborious procedure for largedimensional

systems.

Instead, for non-PPT states, by choosing an appropriate set of operators it is possible

to gain quantitative information about the entanglement by using the inequalities

in [1]. This can then be converted into a lower bound on the negativity.

We then provide different ways this procedure can be carried out, and we give several

examples.

[1] M. Hillery, M. S. Zubairy, Phys. Rev. Lett. 96, 050503 (2006)