# Emergent Gauge Symmetries and Quantum Operations

## TL;DR

This paper explores the connection between emergent gauge symmetries, entropy production, and quantum operations within algebraic quantum physics, revealing a novel duality through subsystem decomposition without tensor products.

## Contribution

It establishes a new link between gauge symmetries and quantum operations using algebraic methods and GNS representation, without relying on tensor product structures.

## Key findings

- Identifies a gauge group acting on a subsystem A
- Links gauge transformations to entropy-increasing quantum operations
- Provides a physical simulation method for the gauge-quantum operation duality

## Abstract

The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This, in turn, has recently led to applications to the study of entanglement in systems of identical particles. In the course of those investigations on entanglement and particle identity, an emergent gauge symmetry has been found by Balachandran, de Queiroz and Vaidya. In this letter we establish a novel connection between that gauge symmetry, entropy production and quantum operations. Thus, let A be a system described by a finite dimensional observable algebra and $\omega$ a mixed faithful state. Using the Gelfand-Naimark-Segal (GNS) representation we construct a canonical purification of $\omega$, allowing us to embed A into a larger system C. Using Tomita-Takasaki theory, we obtain a subsystem decomposition of C into subsystems A and B, without making use of any tensor product structure. We identify a group of transformations that acts as a gauge group on A while at the same time giving rise to entropy increasing quantum operations on C. We provide physical means to simulate this gauge symmetry/quantum operation duality.