Extracting quantum work statistics by single qubit interferometry

Abstract

We first derive the Jarzynski relation [1] between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. We then comment on the information-theoretic underpinning of Jarzynski’s reasoning which helps explain why the Jarzynski relation holds identically both quantumly and classically [2]. We then present a scheme to verify the quantum non-equilibrium fluctuation relations as encapsulated by Jarzynski. We show that the characteristic function of the work distribution of a quantum system (which is basically equal to the Wick rotated average exponential of the thermodynamical work) can be extracted from Ramsey interferometry of a single probe qubit (which need not itself be pure, though it must not be fully depolarized) [3,4].We first derive the Jarzynski relation [1] between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. We then comment on the information-theoretic underpinning of Jarzynski’s reasoning which helps explain why the Jarzynski relation holds identically both quantumly and classically [2]. We then present a scheme to verify the quantum non-equilibrium fluctuation relations as encapsulated by Jarzynski. We show that the characteristic function of the work distribution of a quantum system (which is basically equal to the Wick rotated average exponential of the thermodynamical work) can be extracted from Ramsey interferometry of a single probe qubit (which need not itself be pure, though it must not be fully depolarized) [3,4]. An interesting fact is that while the quantum version of the Jarzynski equality remains satisfied even in the presence of quantum correlations, the individual thermodynamical work moments in the expansion of the free energy are, in fact, sensitive to the genuine quantum correlations [5]. Whether this is a fortuitous coincidence remains to be seen, but it certainly goes towards explaining why the laws of thermodynamics happen to be so robust as to be independent of the underlying micro-physics.We intend to elucidate the subtle connection between Jarzynski’s relation and the “quantum arrow of time”. Finally we comment on the fact that our scheme for measuring the quantum work characteristic function belongs to the computational class known as DCQ1 [6], namely all computations that can be performed with only one pure qubit (and N maximally mixed ones).