Delocalization power of global unitary operations on quantum information

TL;DR

This paper studies how global unitary operations delocalize quantum information and identifies conditions under which one piece of information can be relocalized using LOCC, revealing different non-local properties.

Contribution

It establishes a necessary and sufficient condition for LOCC relocalization, linking it to controlled-unitary equivalence of global unitaries.

Findings

LOCC relocalization is possible iff the unitary is locally equivalent to a controlled-unitary.

Delocalization power differs from entangling power in characterizing non-local properties.

The work provides a criterion to classify global unitaries based on their delocalization capabilities.

Abstract

We investigate how originally localized two pieces of quantum information represented by a tensor product of two unknown qudit states are delocalized by performing two-qudit global unitary operations. To characterize the delocalization power of global unitary operations on quantum information, we analyze the necessary and sufficient condition to deterministically relocalize one of the two pieces of quantum information to its original Hilbert space by using only LOCC. We prove that this LOCC one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent to a controlled-unitary operation. The delocalization power and the entangling power characterize different non-local properties of global unitary operations.