Extractable Work from Correlations

Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory. In this work, we study how to use correlations among quantum systems to optimally store work. We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems. We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations. We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy. Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.

Popular Summary

The field of quantum thermodynamics is aimed at understanding the laws of thermodynamics at the quantum level and hence the interplay between two fundamental theories of physics. A central question in this field of research is whether quantum effects can enhance (or limit) thermodynamic processes. Here, we show that entanglement, a paradigmatic quantum effect, can enhance the extraction of work.

We consider a collection of quantum systems that are individually useless, that is, from which no work can be extracted (i.e., they are “passive”). We start by considering the case of only two qubits, and we generalize our analysis up to $N$ qubits. Quantum theory allows for these systems to be correlated in a genuinely quantum manner: The systems can be entangled with each other. Importantly, thanks to these correlations, the global system can now become useful: We study how correlations among quantum states can be used to store work. We quantify the amount of work that can be extracted from correlations only, showing that quantum correlations (i.e., entanglement) outperform classical correlations. In other words, the amount of work that can be stored in unentangled states is always lower than the amount that can be stored in entangled states. Moreover, in the limit of a large number of systems, this gain vanishes, and one recovers the classical limit.

Our results shed new light on the fundamental problem of what is quantum in quantum thermodynamics, and we expect that our findings will motivate analyses of how different types of entanglement are related to extractable work.

Figure 1

Extractable work from entangled (blue line), separable (red line), and entangled but having the same entropy as the separable (green line) states in units of the initial total energy of the system. Specifically, we take the states Eqs. (7), (8), and (11) for $d=2$, $\beta E_1=1$. As $n$ increases, classical states become able to store essentially the same amount of work as quantum ones.