# Geometric decoherence in diffusive open quantum systems

## TL;DR

This paper investigates the geometric aspects of decoherence in open quantum systems, revealing that decoherence can be a geometric process and proposing control schemes to mitigate it, with implications for robust quantum gate implementation.

## Contribution

It introduces a complex-valued geometric phase for non-unitary evolutions and demonstrates that decoherence can be geometric, providing insights for quantum control and gate robustness.

## Key findings

- Decoherence can be a geometric quantity independent of system dynamics.
- In some models, decoherence is purely dynamical, while in others it is geometric.
- A non-perturbative control scheme can eliminate geometric decoherence.

## Abstract

Based on a generic quantum open system model, we study the geometric nature of decoherence by defining a complex-valued geometric phase through stochastic pure states describing non-unitary, non-cyclic and non-adiabatic evolutions. The ensemble average of the complex geometric phases for the pure stochastic states yields a conventional geometric phase together with an amplitude factor. We show that the decoherence process described by the decaying amplitude can be a geometric quantity independent of the system's dynamics. It is a remarkable fact that the geometric phase of a quantum system can serve as an ideal realisation of quantum gates due to its robustness against dynamical errors, however, in this paper we show that, for some open quantum systems, a desirable geometric phase may be accompanied by an unwanted robust geometric decoherence factor. Two exactly solvable models are studied to demonstrate that, while the decoherence is a purely dynamical effect for a dephasing two-level model, the decoherence in a dissipative two-level model can be a geometric process. Finally, we show that such a geometric decoherence effect may be eliminated by a non-perturbative control scheme.