Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing

TL;DR

This paper links the problem of converting three-party entangled states into two-party states with polynomial identity testing, enabling the use of efficient algorithms from computational complexity to quantum entanglement transformations.

Contribution

It establishes an equivalence between entanglement transformation decision problems and polynomial identity testing, providing a new computational approach.

Findings

Polynomial identity testing can decide entanglement transformations.

Efficient randomized algorithms are applicable to quantum state conversions.

The approach bridges quantum information and computational complexity.

Abstract

We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations.