Quantum fridge works by superposing the order of events

Ever tried defrosting your dinner by popping it in one identical freezer after another? Strange as it sounds, recent studies of indefinite causal order—in which different orders of events are quantum superposed—suggest this could actually work for quantum systems. Researchers at the University of Oxford show how the phenomenon can be put to use in a type of quantum refrigeration.

The results follow reports of the effects of indefinite causal order in quantum computation and quantum communication. "People were asking—is the quantum circuit model a complete description of every possible quantum ordering of events?" explains David Felce, a Ph.D. student at the University of Oxford, as he describes how research into indefinite causal order has emerged over the past 10 years.

Probing this question led to studies of states passing through depolarizing channels in which a well-defined initial state ends up in a totally random state. No meaningful information transfer is possible through a depolarizing channel, but things change when the quantum state is put through one depolarization channel after another in an indefinite causal order. Then the order of the channels is in a superposition, and entangled with a control qubit, which is in a superposition of different states. Researchers have found that when a state is passed through two depolarizing channels in an indefinite causal order, a certain amount of information is transmitted if the control qubit can also be measured.

"Thermalization is quite similar to depolarization," explains Felce, explaining that instead of giving you a completely random state, thermalization gives you a state that is mostly random with a higher or lower chance of being in the higher or lower energy state depending on the temperature. "I thought, if you thermalize something twice in an indefinite causal order, then you won't end up with the temperature state that you would expect." Unexpected temperature outcomes from thermalization could be thermodynamically useful, he adds.

Quantum refrigeration

Felce and University of Oxford Professor of Information Science Vlatko Vedral analyzed expressions for a thermalizing channel described in similar terms to a depolarizing channel and considered the effects of indefinite causal order. Among the "weird" effects they found was the possibility of thermalizing a quantum state with two thermal reservoirs at the same temperature with indefinite causal order and ending up with the state in a different temperature. The researchers propose a refrigeration cycle with this as the first step. Next, it would be necessary to measure the control qubit to find out whether the temperature of the thermalized quantum state has been raised or not. If it has, subsequently thermalizing the same state classically with a hot reservoir (step two) then a cold reservoir (step three) could cool the cold reservoir because the heat transferred from the state back to the cold reservoir would be less than that transferred by the cold reservoirs to the state in step one.

At a glance, this may seem at odds with the laws of thermodynamics. A conventional fridge works because it is plugged into the mains or some other energy source, so what provides the energy for the indefinite causal order quantum refrigeration? Felce explains that this can be described in the same way that Maxwell's demon fits with the laws of thermodynamics.

Maxwell had hypothesized that a demon monitoring the door of a partition in a box of particles could measure the temperature of particles and open and shut the door to sort the cold and hot particles into separate partitions of the box, decreasing the entropy of the system. According to the laws of thermodynamics, entropy should always increase in the absence of work done. Scientists have since explained the apparent inconsistency by highlighting that the demon is measuring the particles, and that the information stored on their measured temperatures will require a certain amount of energy to erase—Landauer's erasure energy.

Felce points out that just like Maxwell's demon, in every cycle of the quantum refrigerator, it is necessary make a measurement on the control qubit to know what order things happened. "Once you have stored this essentially random information in your hard drive, if you want to return your hard drive to its initial state, then you will require energy to erase the hard drive," he says. "So you could think of feeding the fridge empty hard drives, instead of electricity, to run."

Next, Felce plans to look into ways of implementing the indefinite causal order refrigerator. So far, experimental implementations of indefinite causal orders have used control qubits in a superposition of polarization states. A polarization-dependent beamsplitter would then send a photon through a circuit in a different direction depending on the polarization, so that a superposition of polarization states leads to a superposition of the order in which the photon passes through the circuit elements. Felce is also interested in looking into generalizing the results to more reservoirs.