Quantum Discord and Maxwell’s Demons

Quantum discord was proposed as an information theoretic measure of the “quantumness” of correlations. I show that discord determines the difference between the efficiency of quantum and classical Maxwell’s demons in extracting work from collections of correlated quantum systems. Information has an energetic value: It can be converted into work. Maxwell’s demon was introduced into thermodynamics to explore the role of information and, more generally, to investigate the place of “intelligent observers” in physics. In modern discussions of the subject “intelligence” is often regarded as predicated upon or even synonymous with the information processing ability – with computing. Thus, Maxwell’s demon is frequently modelled by a universal Turing machine – a classical computer – endowed with the ability to measure and act depending on the outcome. The role of such a demon is then to implement an appropriate conditional dynamics – to react to the state of the system as revealed through its correlation with the state of the apparatus. It is now known that quantum logic – i.e., logic employed by quantum computers – is in some applications more powerful than its classical counterpart. It is therefore intriguing to enquire whether a quantum demon – an entity that can measure non-local states and implement quantum conditional operations – could be more powerful than a classical one. I show that quantum demons can typically extract more work than classical demons from correlations between quantum systems, and that the difference is given by a variant of the quantum discord, recently introduced measure of the “quantumness” of correlations. Quantum discord is the difference between the two classically identical formulae that measure the information content of a pair of quantum systems. Several closely related variants can be obtained starting from the original definition given in terms of the mutual information. Mutual information is a measure of the strength of correlations between, say, the apparatus A and the system S: I(S : A) = H(S) +H(A)−H(S,A) (1)