Classification of tripartite entanglement with one qubit (9 pages)

Chang‐shui Yu, He-Shan Song

Ashton S. Bradley

Marcio F. Cornelio, A. F. R. de Toledo Piza

We present a method to find the decompositions of tripartite entangled pure states with one qubit which are smaller than two successive Schmidt decompositions. We use this method to get a classification of the entangled states according to their decompositions. Furthermore, we also use this method to classify the entangled states that can be interconverted through stochastic local operations and classical communication. More general tripartite systems are briefly discussed.

A. T. Rezakhani

A. I. Solomon, Choon-Lin Ho

We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley hyper-determinant, and its six associated 2 × 2 subdeterminants. In particular we show that this classification provides a necessary and sufficient condition for separability.

Steven T. Flammia, Animesh Datta