Decoherence in open Majorana systems

TL;DR

This paper shows that in Gaussian fermionic systems, decoherence caused by thermal baths occurs at a temperature-independent rate, challenging the idea that lowering temperature can suppress decoherence in Majorana-based qubits.

Contribution

The study provides a microscopic derivation of Markovian master equations for Gaussian fermions, revealing temperature-independent decoherence dynamics in Majorana systems.

Findings

Decoherence rate is independent of bath temperature.

Gaussian fermionic systems cannot have thermal decoherence suppressed by cooling.

Markovian dynamics are derived using covariance matrices.

Abstract

Coupling to a thermal bath leads to decoherence of stored quantum information. For a system of Gaussian fermions, the fermionic analog of linear or Gaussian optics, these dynamics can be elegantly and efficiently described by evolution of the system's covariance matrix. Taking both system and bath to be Gaussian fermionic, we observe that decoherence occurs at a rate that is independent of the bath temperature. Furthermore, we also consider a weak coupling regime where the dynamics are Markovian. We present a microscopic derivation of Markovian master equations entirely in the language of covariance matrices, where temperature independence remains manifest. This is radically different from behaviour seen in other scenarios, such as when fermions interact with a bosonic bath. Our analysis applies to many Majorana fermion systems that have been heralded as very robust, topologically protected, qubits. In these systems, it has been claimed that thermal decoherence can be exponentially suppressed by reducing temperature, but we find Gaussian decoherence cannot be cooled away.