Reversibility and the structure of the local state space

TL;DR

This paper investigates how reversibility constrains the structure of local and global state spaces in quantum and generalized theories, revealing that non-trivial reversible dynamics are limited to certain reducible or classical systems.

Contribution

It establishes conditions under which reversible dynamics are trivial or non-trivial, linking reversibility to the geometry and non-locality of state spaces in operational theories.

Findings

Reversible dynamics are trivial in maximally non-local theories with certain local state space properties.

Classical systems are uniquely capable of supporting non-trivial reversible dynamics among regular polytope state spaces.

Non-trivial reversible dynamics can exist in theories with reducible state spaces, but reversible entanglement generation remains impossible.

Abstract

The richness of quantum theory's reversible dynamics is one of its unique operational characteristics, with recent results suggesting deep links between the theory's reversible dynamics, its local state space and the degree of non-locality it permits. We explore the delicate interplay between these features, demonstrating that reversibility places strong constraints on both the local and global state space. Firstly, we show that reversible dynamics are trivial (composed of local transformations and permutations of subsytems) in maximally non-local theories whose local state spaces satisfy a dichotomy criterion; this applies to a range of operational models that have previously been studied, such as d-dimensional "hyperballs" and almost all regular polytope systems. By separately deriving a similar result for odd-sided polygons, we show that classical systems are the only regular polytope state spaces whose maximally non-local composites allow for non-trivial reversible dynamics. Secondly, we show that non-trivial reversible dynamics do exist in maximally non-local theories whose state spaces are reducible into two or more smaller spaces. We conjecture that this is a necessary condition for the existence of such dynamics, but that reversible entanglement generation remains impossible even in this scenario.