A generalization of Schmidt number for multipartite states

TL;DR

This paper introduces a generalized Schmidt number for multipartite quantum states, applicable to pure and mixed states of any number of parties and dimensions, enhancing entanglement characterization.

Contribution

It proposes a new multipartite Schmidt number and coefficients, extending the bipartite concept to more complex quantum systems with proven entanglement monotonicity.

Findings

The generalized Schmidt number is valid for pure and mixed states.

It is entanglement monotonic.

Applicable to arbitrary multipartite systems.

Abstract

The Schmidt number is of crucial importance in characterizing the bipartite pure states. We explore and propose here a generalization of Schmidt number for states in multipartite systems. It is shown to be entanglement monotonic and valid for both pure and mixed states. In addition, the corresponding generalization of multipartite Schmidt coefficients is introduced. Our approach is applicable for systems with arbitrary number of parties and for arbitrary dimensions.