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Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot body to the cold one), posing an apparent challenge to the second law of thermodynamics. Such an “anomalous” heat current was observed in a recent experiment (K. Micadei et al., arXiv:1711.03323), by employing two spin systems initially quantum correlated. Nevertheless, the precise relationship between this intriguing phenomenon and the initial conditions that allow it is not fully evident. Here, we address energy transfer in a wider perspective, identifying a nonclassical contribution that applies to the reversion of the heat flow as well as to more general forms of energy exchange. We derive three theorems that describe the energy transfer between two microscopic systems, for arbitrary initial bipartite states. Using these theorems, we obtain an analytical bound showing that certain type of quantum coherence can optimize such a process, outperforming incoherent states. This genuine quantum advantage is corroborated through a characterization of the energy transfer between two qubits. For this system, it is shown that a large enough amount of coherence is necessary and sufficient to revert the thermodynamic arrow of time. As a second crucial consequence of the presented theorems, we introduce a class of nonequilibrium states that only allow unidirectional energy flow. In this way, we broaden the set where the standard Clausius statement of the second law applies.

Discrete quantum feedback control consists of a managed dynamics according to the information acquired by a previous measurement. Energy fluctuations along such dynamics satisfy generalized fluctuation relations, which are useful tools to study the thermodynamics of systems far away from equilibrium. Due to the practical challenge to assess energy fluctuations in the quantum scenario, the experimental verification of detailed fluctuation relations in the presence of feedback control remains elusive. We present a feasible method to experimentally verify detailed fluctuation relations for discrete feedback control quantum dynamics. Two detailed fluctuation relations are developed and employed. The method is based on a quantum interferometric strategy that allows the verification of fluctuation relations in the presence of feedback control. An analytical example to illustrate the applicability of the method is discussed. The comprehensive technique introduced here can be experimentally implemented at a microscale with the current technology in a variety of experimental platforms.

Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with the same amount of resources (in terms of effective Hilbert space dimension), various models of quantum walks. All the algorithms developed within quantum walk models are thus directly inherited by the quantum cellular automata. The latter, however, has its structure based on local interactions between qubits, and as such it can be more suitable for present (and future) experimental implementations.