In an incredible scientific breakthrough, researchers from Duke University have completely reinvented Bayes’ rule. Originally defined by Thomas Bayes in 1763, they’ve since combined it with the tenets of quantum mechanics. Dealing with conditional probabilities, the quantum Bayes’ rule offers a fascinating – and somewhat exotic – way to think about conditioned probabilities. Among other reasons, this new approach is important for both theoretical and applied physics. This work was a collaboration between Professor Valerio Scarani, Assistant Professor Ge Bai, and Professor Francesco Buscemi. They released it into the wild, as it were, Phys. Rev. Lett.
Thomas Bayes first articulated his probability theorem in “An Essay Towards Solving a Problem in the Doctrine of Chances.” His rule has since become a vital tool for guiding decision making. It enables more informed predictions by using past experience to predict future outcomes. Virtually for 250 years, it’s been an integral part of disciplines such as statistics and one of the foundations in the world of statistical machine learning.
The quantum version of Bayes’ rule that has been newly proposed starts from the quantum analog to the minimum change principle. This principle is intimately connected to the Petz transpose map, which was invented by Dénes Petz in the 1980s. Figure 1: Petz map quantum circuit The Petz map has already demonstrated great potential in quantum computing applications — specifically for quantum error correction and machine learning tasks.
Professor Valerio Scarani of Singapore announced the importance of this breakthrough. As principal investigator at NUS’s Center for Quantum Technologies, he is a member of the NUS Department of Physics and Deputy Director of the CQT.
“I would say it is a breakthrough in mathematical physics,” – Professor Valerio Scarani
In doing so, the research team has uncovered something remarkable. For the first time, they have mathematically derived Bayes’ rule from a more fundamental principle, an achievement that represents a monumental advance in the understanding of quantum probabilities. Scarani stressed how reinforcing it would be to know that they are using the Petz map as a framework for making sense of all these new developments.
Professor Francesco Buscemi was equally excited about the potential implications of their work.
“Bayes’ rule has been helping us make smarter guesses for 250 years. Now we have taught it some quantum tricks,” – Prof Buscemi
Our newly formulated quantum Bayes’ rule provides a powerful theoretical foundation. Equally significant is what it unlocks for more exciting real-world uses in the fast-moving quantum computing industry. These distinct features of the Petz map – a combination of intentionality and fortuity – set the stage for this novel, arts-driven approach.
The authors have made their research publicly available on arXiv, which you can access using this DOI 10.48550/arxiv.2410.00319. Since then they’ve made their work public in Physical Review Letters DOI 10.1103/5n4p-bxhm.