Is there an observer-independent time-reversal in physics? Only for Hamiltonian dynamics, we argue. Otherwise there’s only retrodiction, which of course depends on the retrodictor’s (prior) believes. The paper (co-authored with Clive C. Aw and Valerio Scarani) is freely available from AVS Quantum Science website, where it is highlighted as a Featured Article. Below is a talk I recently gave on these ideas.

I was recently invited to give an overview talk on Petz’s “transpose” or “recovery” map at the workshop Workshop on Quantum Information and Quantum Black Holes, organized by Norihiro Iizuka (Osaka) and Tomonori Ugajin (Kyoto). I’ve put together what I came to learn about the properties of Petz’s transpose map, its uses is various areas of information theory and physics, and (most importantly!) its conceptual meaning. Slides are available here. Mark Wilde’s textbook contains a chapter entirely devoted to the technical aspects of Petz’s map and the theory of approximate recoverability.

2025/4/22 Update: in these four years, we’ve learned a lot more about the Petz transpose map, especially its interpretation and relationship to Bayesian inversion. I’ve thus updated the slides to include at least the pointer to these new papers. The most important (in my opinion) is the derivation of the Petz transpose map from a principle of minimum change. The original slides presented in the video are still available at this link.

“The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it to collapse in deepest humiliation.”

― Arthur Eddington, The Nature of the Physical World, Chap. 4

But why is that so? Why is the Second Law so “special” among the other laws of physics?

Simply because—as we argue in a paper recently published on Physical Review E and freely available on the arXiv—the Second Law is not so much about physics, as it is about logic and consistent reasoning. More precisely, we argue that the Second Law can be seen as the shadow of a deeper asymmetry that exists in statistical inference between prediction and retrodiction, and ultimately imposed by the consistency of the Bayes–Laplace Rule.

A little bit of background. In the past two decades, thermodynamics has undergone unprecedented progresses. These can be traced back to the developments of stochastic thermodynamics, on the one hand, and the theory of nonequilibrium fluctuations, on the other. The latter, in particular, has shown that the Second Law emerges from a more fundamental “balance relation” between a physical process and its reverse. According to such a balance relation, for example, scrambled eggs are not forbidden to unscramble spontaneously—instead, the probability of such a process is just extremely tiny, compared with that of its more familiar reverse. In turn, entropy—i.e. the thing that “no one knows what it really is”, according to the apocryphal exchange between Shannon and von Neumann—precisely is a measure of such a disparity.

In this paper we go one step further and show that the existence of a disparity is not due to some kind of “physical propensity” that irreversible processes have for unfolding in one direction more likely than in the opposite direction—an explanation that would lead to a circular argument—, but to the intrinsic asymmetry that exists between prediction and retrodiction in inferential logic. We thus conclude that the foundations of the Second Law are not to be found within physics, but one step below, at the level of logic.

A nice little piece written by CQT/NUS outreach is also available here.

One month ago I gave a colloquium at the 13th Annual Symposium of the Centre for Quantum Technologies (CQT) in Singapore. I decided to speak about my recent work on the role of Bayesian retrodiction in statistical mechanics — more precisely, in the conceptual foundations underlying fluctuation relations and the second law of thermodynamics.

The preprint is available on the arXiv: https://arxiv.org/abs/2009.02849

Given at the Asian Quantum Information Science Conference 2020 (link).

This colloquium, aimed at an audience with basic knowledge about quantum theory but not necessarily familiar with the topic, was given for the Online Colloquium Series of the School of Computational Science of the Korea Institute for Advanced Study (KIAS).

Incompatibility of quantum measurements lies at the core of nearly all quantum phenomena, from Heisenberg’s Uncertainty Principle, to the violation of Bell inequalities, and all the way up to quantum computational speed-ups.  Historically, quantum incompatibility has been considered only in a qualitative sense.  However, recently various resource-theoretic approaches have been proposed that aim to capture incompatibility in an operational and quantitative manner.  Previous results in this direction have focused on particular subsets of quantum measurements, leaving large parts of the total picture uncharted.

A work, which I wrote together with Eric Chitambar and Wenbin Zhou and was published yesterday on Physical Review Letters, proposes the first complete solution to this problem by formulating a resource theory of measurement incompatibility that allows free convertibility among all compatible measurements.  As a result, we are now able to explain quantum incompatibility in terms of quantum programmability; namely, the ability to switch on the fly between incompatible measurements is seen as a resource.  From this perspective, quantum measurement incompatibility is intrinsically a dynamical phenomenon that reveals itself in time as we try to control the system.

Read about this on Physical Review Letters or, for free, on the arXiv.