Classification of the Entangled states L\times N\times N

Abstract

We presented a general classification scheme for the tripartite $L\times N\times N$ entangled system under stochastic local operation and classical communication. The whole classification procedure consists of two correlated parts: the simultaneous similarity transformation of a commuting matrix pair into a canonical form and the study of internal symmetry of parameters in the canonical form. Based on this scheme, a concrete example of entanglement classification for a $3\times N\times N$ system is given.

21 pages; published in Phys. Rev. A

References in corpus (4)

• Complexity of matrix problems
• Pairs of mutually annihilating operators
• The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System
• Classification of the Entangled States of $2\times N\times N$

Cited by in corpus (6)

• Entanglement Classification of Four-partite States under the SLOCC
• Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Quantum State Concentration and Classification of Multipartite Entanglement
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Classification of the Entangled States of $2\times L\times M\times N\times H$