Quantum Relativity of Subsystems

TL;DR

This paper investigates how quantum reference frames influence the definition and properties of subsystems and entanglement, revealing that subsystem notions are frame-dependent and affected by symmetry constraints in quantum systems.

Contribution

It introduces a gauge-invariant, frame-dependent framework for understanding subsystems and entanglement in quantum reference frames, highlighting the relativity of subsystem locality.

Findings

Different QRF perspectives lead to different subsystem algebras.

Symmetry constraints can change commuting algebras into non-commuting ones.

Subsystem locality is frame-dependent and not invariant under QRF transformations.

Abstract

One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. We further demonstrate that subalgebras which commute before imposing the symmetry constraint can translate into non-commuting algebras in a given QRF perspective after symmetry imposition. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.