Original sentence: A Werner state is a  dimensional bipartite quantum state that is invariant under the unitary  for any unitary.All entangled Werner states violate the  PPT separability criterion, but for  no Werner states violate the weaker reduction criterion.An N-party Werner state is a state that is invariant under U⊗U⊗...⊗U for any unitary U on a single subsystem.That is, a state  that satisfies.The Werner state is no longer described by a single parameter, but by  parameters, and is a linear combination of the N.The Werner states are mixtures of projectors onto the symmetric- and anti-symmetric subspaces, with the relative weight being the only parameter that defines the state.Werner states are separable for  and entangled for.for all  on the d-dimensional subsystems.where the new parameter  varies between -1 and 1 and relates to the  above as
Edited sentence: A Werner state is a  dimensional bipartite quantum state that is invariant under the unitary  for any unitary U.All entangled Werner states violate the  PPT separability criterion, but for d ≥ 3 no Werner states violate the weaker reduction criterion.An N-party Werner state is a state that is invariant under  for any unitary U on a single subsystem.That is, a state ρ that satisfies.The Werner state is no longer described by a single parameter, but by N.The Werner states are mixtures of projectors onto the symmetric and antisymmetric subspaces, with the relative weight psym being the only parameter that defines the state.Werner states are separable for psym ≥  and entangled for pas <.for all U on the d-dimensional subsystems.where the new parameter α varies between −1 and 1 and relates to psym as.− 1 parameters, and is a linear combination of the N