Fluctuation theorems for quantum processes

TL;DR

This paper develops fluctuation theorems for quantum processes, extending thermodynamic relations like Jarzynski and Crooks to quantum systems with feedback, and demonstrates their application to superconducting qubits.

Contribution

It introduces quantum fluctuation theorems for CPTP maps with feedback, clarifies conditions for reverse processes, and applies the theory to superconducting qubits.

Findings

Derived quantum Jarzynski equality and Crooks theorem.

Identified unitality as a key condition for reverse process physicality.

Applied the theory to extract system-bath coupling in superconducting qubits.

Abstract

We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving (CPTP) maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.