Disentangling tensor product structures

TL;DR

This paper investigates how changing the tensor product structure in finite-dimensional Hilbert spaces influences entanglement, demonstrating the possibility of disentangling structures in specific cases but not generally.

Contribution

It provides a constructive example of disentangling tensor product structures for a C-NOT gate, and proves limitations for most quantum evolutions.

Findings

Disentangling tensor structures is possible in specific quantum gate evolutions.

Most time-evolving states cannot be disentangled by changing tensor structures.

The study advances understanding of quantum mereology and entanglement manipulation.

Abstract

As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state, there exists a tensor product structure in which no entanglement is generated. We give a concrete, constructive example of disentangling tensor product structure in the case of a C-NOT gate evolution between two qbits, before showing that this cannot be achieved for most time-evolving quantum states.