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Experimental demonstration of information to energy conversion in a quantum system at the Landauer Limit

Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance setup to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins $S=1/2$ (qubits) molecule ---the system, the reservoir and the ancilla--- to measure the heat dissipated during the implementation of a global system-reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way we were able to verify that an operation that changes the information content of the system must necessary generate heat in the reservoir, exactly as predicted by Landauer's principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors.