Matrix Product States: Entanglement, symmetries, and state transformations

Understand

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).