Quantum Symmetries and Cartan Decompositions in Arbitrary Dimensions

TL;DR

This paper explores the connection between Cartan decompositions and quantum symmetries, introducing a new method to extend the concurrence canonical decomposition to multipartite systems with arbitrary dimensions.

Contribution

It presents a novel general method to derive Cartan decompositions for multipartite quantum systems from single subsystem decompositions, extending the CCD to arbitrary dimensions.

Findings

Established a correspondence between Cartan decompositions and quantum symmetries.

Developed a new odd-even type decomposition for multipartite systems.

Extended the concurrence canonical decomposition to systems with subsystems of arbitrary dimension.

Abstract

We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application, we describe a new and general method to obtain Cartan decompositions of the unitary group of evolutions of multipartite systems from Cartan decompositions on the single subsystems. The resulting decomposition, which we call of the odd-even type, contains, as a special case, the concurrence canonical decomposition (CCD) presented in the context of entanglement theory. The CCD is therefore extended from the case of a multipartite system of n qubits to the case where the component subsystems have arbitrary dimension.