Tripartite entanglement transformations and tensor rank

Understand

Understanding the nature of multipartite entanglement is a central mission of quantum information theory.

• To this end, we investigate the question of tripartite entanglement convertibility.
• We find that there exists no easy criterion to determine whether a general tripartite transformation can be performed with a nonzero success probability and in fact, the problem is NP-hard.
• Our results are based on the connections between multipartite entanglement and tensor rank (also called Schmidt rank), a key concept in algebraic complexity theory.