Simulating Symmetric Time Evolution With Local Operations

TL;DR

This paper introduces a novel entanglement-based approach to analyze symmetry properties and transition possibilities in open quantum systems, bypassing traditional group theory methods and revealing new conserved quantities.

Contribution

It develops a new method using entanglement to study dynamic symmetries, applicable to any semi-simple Lie group, and identifies entanglement as a conserved quantity under reversible transformations.

Findings

Entanglement of bipartite images is conserved under reversible transformations.

The method applies to general symmetries beyond specific groups.

New conserved quantities differ from traditional Hamiltonian-based ones.

Abstract

In closed systems, dynamical symmetries lead to conservation laws. However, conservation laws are not applicable to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given two states, the transition from one state to the other is possible. The usual approach to the problem of finding such rules relies heavily on group theory and involves a detailed study of the structure of the respective symmetry group. We approach the problem in a completely new way by using entanglement to investigate the asymmetry properties of quantum states. To this end, we embed the space state of the system in a tensor product Hilbert space, whereby symmetric transformations between two states are replaced with local operations on their bipartite images.The embedding enables us to use the well-studied theory of entanglement to investigate the consequences of dynamic symmetries. Moreover, under reversible transformations, the entanglement of the bipartite image states becomes a conserved quantity. These entanglement-based conserved quantities are new and different from the conserved quantities based on expectation values of the Hamiltonian symmetry generators. Our method is not group-specific and applies to general symmetries associated with any semi-simple Lie group.