Local manipulation of multipartite entanglement

Many applications of quantum information rely on the potentiality of quantum systems to be correlated. For pure states, these correlations coincide with entanglement. Hence, the qualification and quantification of multipartite entanglement is one of the central topics within quantum information. However, as the dimension of the Hilbert space grows exponential with the number of considered subsystems, many very fundamental questions in this context are still unanswered.

In this talk I will focus on the local manipulation of multipartite entanglement contained in systems which are composed of n d-level subsystems [1,2,3]. Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of entanglement. I will present the characterization of almost all LOCC transformations among pure states describing arbitrarily many subsystems which are of arbitrary local dimension (d). I will explain that non-trivial LOCC transformations among generic fully entangled pure states are almost never possible. Hence, almost all multipartite states are isolated. They can neither be deterministically obtained from local unitary (LU)-inequivalent states via local operations, nor can they be deterministically transformed to pure fully entangled LU-inequivalent states. I will then present a simple expression for the maximal probability to convert one multi-qudit fully entangled state to another for this generic set of states. The consequences of these findings in the context of entanglement theory will be discussed.

[1] G. Gour, B. Kraus, N. R. Wallach, J. Math. Phys. 58, 092204 (2017)
[2] D. Sauerwein, N. R. Wallach, G. Gour, B. Kraus, in preparation (2017).
[3] J. I. de Vicente, C. Spee, and B. Kraus, Phys. Rev. Lett. 111, 110502 (2013)