PIRSA:16060097

An algebraic classification of entangled states

Buniy, R. (2016). An algebraic classification of entangled states. Perimeter Institute. https://pirsa.org/16060097

Buniy, Roman. An algebraic classification of entangled states. Perimeter Institute, Jun. 13, 2016, https://pirsa.org/16060097 

          @misc{ pirsa_PIRSA:16060097,
            doi = {10.48660/16060097},
            url = {https://pirsa.org/16060097},
            author = {Buniy, Roman},
            keywords = {Quantum Foundations},
            language = {en},
            title = {An algebraic classification of entangled states},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {jun},
            note = {PIRSA:16060097 see, \url{https://pirsa.org}}
          }

Roman Buniy

Chapman University

Talk number
PIRSA:16060097
Collection
Talk Type
Subject
Abstract

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.