PIRSA:16060097 Scientific Series Quantum Foundations

DOI10.48660/16060097

Series: Quantum Foundations

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}}
}

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.

 

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