Anomalous Heat Flows and Quantum Otto Engine with (In)definite Causal Order

The principle that heat spontaneously flows from higher temperatures to lower temperatures is a cornerstone of classical thermodynamics. While this principle holds true for macroscopic systems at equilibrium, here we show that, when a quantum system undergoes two thermalization processes in an indefinite causal order, it can absorb heat even if its initial temperature was higher than the temperature of the reservoirs involved in the two thermalizations. Exploiting this anomalous heat flow, we design a quantum Otto cycle with indefinite causal order, which generates work and simultaneously achieves refrigeration. These unconventional features can be achieved by a process with indefinite causal order known as the quantum switch, but are not uniquely associated to indefinite causal order. In general, we prove that the action of two thermalizations in a quantum switch can be exactly reproduced by letting the two thermalizations act in parallel in an equivalent, causally ordered quantum circuit. Compared to its causally ordered counterpart, however, the quantum switch setup is more friendly to free-space photonic implementations. To illustrate this fact, we experimentally realize two photonic setups that reproduce the anomalous heat flow and the quantum Otto cycle with indefinite causal order, respectively.