The time symmetry of quantum mechanics is compatible with the irreversibility of thermodynamics

Mechanics

Technology Innovation Website Editor – 03/14/2022

The experiment shows that the time irreversibility to which we are accustomed can emerge from the reversibility already demonstrated in quantum physics experiments.
[Imagem: Chiara Marletto et al. – 10.1103/PhysRevLett.128.080401]

The time that comes and the time that does not come

Although philosophers have wondered for millennia why time can’t go backwards, the known laws of physics are exactly the same with respect to time – there would be no such thing as an arrow of time traveling relentlessly from the past to the future.

It’s called “time symmetry”: the mathematical laws of physics work just as well for events that follow their deterministic path in the future as they did in the past. This means, for modern physics, that physical processes can be “rewritten” in time and still make sense.

But this is not what we see in everyday reality, in the dimensions of physical space and in the time scale of humans. When we include thermodynamics and entropy, we note that it is not possible to restore the initial conditions of the system.

A typical example of a definition of irreversibility was given by the Joule experiment: a volume of water can be mechanically heated, but not cooled. The concept of a rotating machine performing a transformation was popularized by von Neumann, in the so-called construction, a system capable of performing a certain task in another system and still being able to repeat the action. Thus, transformation is only possible if there is a constructor capable of implementing it.

But how do you reconcile the two? Experiments involving thermodynamics have demonstrated that it is irreversible, while experiments in quantum mechanics have demonstrated the possibility of temporal reversal.

Chiara Marlito and her colleagues at the National Institute for Research in Metrology in Italy and the University of Oxford in the United Kingdom believe they have found a description of the smooth transition between these two domains.

According to the team, there is no conflict between the laws of irreversibility and the laws of time-symmetric reversal of quantum mechanics.

Irreversibility

First of all, the irreversibility was defined as the fact that the transformation T can be performed arbitrarily by a periodic machine, but the same is not true for the inverse of T ~ – in other words, the irreversibility depends on the von Neumann constructor.

To show the concordance between the irreversibility defined in this way and the symmetrical time-reversal laws of quantum mechanics, the researchers studied a qubit-based model that focuses on a quantum homogenizer, that is, a machine made up of an N-qubit set, each one identically prepared in a given state.

By interacting with N qubits in the homogenizer, through quantum gates capable of partial exchange of states of two qubits, the state of a particular Q qubit can be stably shifted (isolated from any heat exchange) in the homogenizer, simultaneously performing a small modification to the device.

If our T is the ‘pure to mixed’ transformation, i.e. in which Q goes from a pure to an maximally mixed state, then it can be shown that this quantum homogenizer meets the criteria for which it must be considered a suitable constructor, while the same is not true For the case T ~ (the “mixed to pure” state). This means that although T is possible, its counterpart T ~ is not, so we restore the irreversibility even in a scenario along the lines of reversible laws at the time,” the team explained.

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The experimental setup the team used to demonstrate in action their new theory that makes the two fields compatible.
[Imagem: Chiara Marletto et al. – 10.1103/PhysRevLett.128.080401]

The emergence of the irreversibility of quantum mechanics

To prove this quantitatively, the researchers conducted an experiment to probe a high-resolution single-photon (1,550 nm) from qubits generated by a low-noise source emitting single photons coupled to an optical fiber.

The interaction between the Q qubit and the three-qubit homogenizer was obtained by sequencing three 50:50 fiber beam splitters, the outputs of which were detected by single photon diodes (InGaAs/InP). Finally, the detector outputs are sent to a time-matched unit of measurement.

With this setup, they first studied the performance of a quantum homogenizer of different quantum partial gate densities, and then evaluated—for both T and T~—the machine’s accuracy in performing the task and its flexibility for repeated use.

By doing so, the researchers confirmed their theoretical predictions and numerical simulations, showing that while a quantum homolog of T might qualify as a constructor, one for ~T degrades too quickly, unable to carry out the transformation.

The team’s conclusion is that this can be seen as clear evidence of the compatibility between constructor-based irreversibility and the time-reversal laws of quantum theory, giving a new perspective on the emergence of thermodynamic irreversibility within a quantum mechanical framework.

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