Matrix Product States: Entanglement, symmetries, and state transformations

Abstract

We analyze entanglement in the family of translationally-invariant matrix product states (MPS). We give a criterion to determine when two states can be transformed into each other by SLOCC transformations, a central question in entanglement theory. We use that criterion to determine SLOCC classes, and explicitly carry out this classification for the simplest, non-trivial MPS. We also characterize all symmetries of MPS, both global and local (inhomogeneous). We illustrate our results with examples of states that are relevant in different physical contexts.

arXiv comment5 + 12 pages; 2 figures

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Cited by in corpus (11)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Symmetries and entanglement of stabilizer states
• State transformations within entanglement classes containing permutation-symmetric states
• A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
• Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Symmetries and local transformations of translationally invariant Matrix Product States
• Measurement-based quantum computation using two-component BECs
• Topological Dipole Insulator
• Identifying families of multipartite states with non-trivial local entanglement transformations
• TTNOpt: Tree tensor network package for high-rank tensor compression