Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing

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.

References in corpus (5)

• Entanglement of assistance and multipartite state distillation
• Deterministic Entanglement of Assistance and Monogamy Constraints
• Tripartite entanglement transformations and tensor rank
• Random bipartite entanglement from W and W-like states
• Entanglement combing

Cited by in corpus (7)

• Multi-copy and stochastic transformation of multipartite pure states
• Randomly distilling W-class states into general configurations of two-party entanglement
• Construction of genuine multipartite entangled states
• Weighted slice rank and a minimax correspondence to Strassen's spectra
• Persistent Tensors and Multiqudit Entanglement Transformation
• Classifying Entanglement by Algebraic Geometry
• Tripartite-to-bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces