A group of INRiM scientists, in collaboration with Oxford University, establishes the compatibility between quantum mechanics’ time-reversal symmetric laws and irreversibility. The study was published in the American Physical Society’s Physical Review Letters.
The topic of irreversibility has been handled in different ways, ranging from statistical mechanics methods to data-theoretic explanations of logically irreversible tasks, in addition to classical and quantum thermodynamics second laws. However, there has always been a concern at the microscopic scale between the irreversible phenomena modelization and the time-reversible quantum laws.
According to this study, irreversibility has been put forth as the fact that a transformation T could be recognized subjectively well by a cyclic machine; however, the same is not possible for T~ (inverse of T). A perfect example of the irreversibility is specified by Joule’s experiment: a volume of water can only be mechanically heated, but cannot be cooled down.
The idea of a cyclic machine going through a transformation was generalized to a constructor by von Neumann. According to the generalization, a system is capable of performing a specific task on another system while remaining capable of repeating the method.
Thus, a transformation can exist only if there is a constructor capable of realizing it. In this research, the irreversibility, according to Joule’s experiment’s generalization, is called constructor-based irreversibility.
To reveal the compatibility between this recently characterized irreversibility and the time-reversal-symmetric laws of quantum mechanics, the team studied a qubit-based toy model centered on the quantum homogenizer, which is a machine that is composed of a set of N qubits — each prepared identically in a particular state.
Interacting with the N qubits of the homogenizer through consequent partial SWAPs (quantum gates capable of partially swapping the states of two qubits), the state of a particular qubit Q can be adiabatically transformed into the homogenizer one, simultaneously prompting a small change in the machine.
If the T is the “pure-to-mixed” transformation — the one where Q transforms from a pure state to a maximally mixed one—it can be evidenced that this quantum homogenizer fulfills the conditions to be regarded as a proper constructor, whereas the same is not possible for the one realizing T~ (in the “mixed-to-pure” scenario).
This implies that even if T is possible, its counterpart T~ is not. Therefore, the team has recovered irreversibility even in a case demonstrated by time-reversible laws.
To quantitatively exhibit this, the team experimented with high-accuracy single-photon qubits, produced by a low-noise prototype source at 1550 nm expelling fiber-coupled single photons.
The interaction between qubit Q and an N = 3 quantum homogenizer was acquired by cascading three 50:50 fiber beam splitters, for which the outputs are identified by InGaAs/InP single-photon avalanche diodes. Lastly, the outputs of the detectors are directed to a time-tagging coincidence module.
Using this setup, the team examined the quantum homogenizer performances for various intensities of the partial SWAP gate. As a result, it evaluated the machine’s accuracy for both T and T~ in the task realization and its resilience to frequent usages.
With this experiment, scientists established their theoretical predictions and numerical simulations. Through this, they exhibited that when the quantum homogenizer for T can be suitable as a constructor, the one for T~ declines too quickly, ultimately not being capable of performing such a transformation.
This could be considered as solid evidence of the compatibility between constructor-based irreversibility and quantum theory time-reversible laws, which offers a new perspective on the thermodynamical irreversibility emergence in a quantum mechanical framework.
Marletto, C., et al., (2022) Emergence of Constructor-Based Irreversibility in Quantum Systems: Theory and Experiment. Physical Review Letters. doi.org/10.1103/PhysRevLett.128.080401.