Local channels preserving maximal entanglement or Schmidt number

TL;DR

This paper proves that local channels preserving maximal entanglement or fixed Schmidt number states must be local unitaries, highlighting the unique role of unitary operations in quantum state preservation.

Contribution

It establishes a necessary and sufficient condition for local channels to preserve maximal entanglement or fixed Schmidt number states, showing they must be local unitaries.

Findings

Local channels preserving MES are local unitaries.

Local channels preserving fixed Schmidt number states are local unitaries.

The result emphasizes the special role of unitary operations in quantum state preservation.

Abstract

Maximal entanglement and Schmidt number play an important role in various quantum information tasks. In this paper, it is shown that a local channel preserves maximal entanglement state(MES) or preserves pure states with Schmidt number $r$($r$ is a fixed integer) if and only if it is a local unitary operation.