{"id":433190,"date":"2025-09-18T08:23:10","date_gmt":"2025-09-18T08:23:10","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/433190\/"},"modified":"2025-09-18T08:23:10","modified_gmt":"2025-09-18T08:23:10","slug":"a-250-year-old-theory-learns-new-tricks","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/433190\/","title":{"rendered":"A 250-Year-Old Theory Learns New Tricks"},"content":{"rendered":"

\t\t\"Probability<\/a>Physicists have derived a quantum version of Bayes\u2019 rule, revealing how beliefs and probabilities update in the quantum realm with potential applications in computing and beyond. Credit: Shutterstock<\/p>\n

An international team of researchers has identified a quantum counterpart to Bayes\u2019 rule.<\/strong><\/p>\n

The likelihood you assign to an event is influenced by what you already believe about the surrounding conditions. This is the basic principle of Bayes\u2019 rule, a method for calculating probabilities first introduced in 1763. An international group of scientists has now demonstrated how this rule also applies within the realm of quantum physics.<\/p>\n

\u201cI would say it is a breakthrough in mathematical physics,\u201d said Professor Valerio Scarani, Deputy Director and Principal Investigator at the Centre for Quantum Technologies, and member of the team. His co-authors on the work published in Physical Review Letters are Assistant Professor Ge Bai at the Hong Kong University of Science and Technology in China, and Professor Francesco Buscemi at Nagoya University in Japan.<\/p>\n

\u201cBayes\u2019 rule has been helping us make smarter guesses for 250 years. Now we have taught it some quantum tricks,\u201d said Prof Buscemi.<\/p>\n

While researchers before them had proposed quantum analogues for Bayes\u2019 rule, they are the first to derive a quantum Bayes\u2019 rule from a fundamental principle.<\/p>\n

Conditional probability<\/p>\n

Bayes\u2019 rule takes its name from Thomas Bayes, who first described conditional probability in \u2018An Essay Towards Solving a Problem in the Doctrine of Chances\u2019.<\/p>\n

Imagine a situation where someone receives a positive flu test. They might have already suspected illness, but the test result shifts how they assess their condition. Bayes\u2019 rule offers a framework for calculating the likelihood of flu that accounts not only for the test outcome and the chance of error but also for the person\u2019s prior assumptions.<\/p>\n

\"Illustration<\/a>What would Thomas Bayes think? In 1763, he proposed a new approach to calculate probabilities. An international team has now updated his ideas to deliver a quantum Bayes\u2019 rule. Credit: Centre for Quantum Technologies<\/p>\n

The rule treats probability as a measure of belief in the likelihood of an event. This perspective has been controversial, since some statisticians argue that probability should represent something \u201cobjective\u201d rather than belief-based. Still, when prior knowledge and assumptions matter, Bayes\u2019 rule serves as a widely accepted reasoning tool. For this reason, it has become essential in fields ranging from medicine and meteorology to data science and machine learning.<\/p>\n

Principle of minimum change<\/p>\n

When calculating probabilities with Bayes\u2019 rule, the principle of minimum change is obeyed. Mathematically, the principle of minimum change minimizes the distance between the joint probability distributions of the initial and updated belief. Intuitively, this is the idea that for any new piece of information, beliefs are updated in the smallest possible way that is compatible with the new facts. In the case of the flu test, for example, a negative test would not imply that the person is healthy, but rather that they are less likely to have the flu.<\/p>\n

In their work, Prof Scarani, who is also from NUS Department of Physics, Asst Prof Bai, and Prof Buscemi began with a quantum analogue to the minimum change principle. They quantified change in terms of quantum fidelity, which is a measure of the closeness between quantum states.<\/p>\n

Researchers always thought a quantum Bayes\u2019 rule should exist because quantum states define probabilities. For example, the quantum state of a particle provides the probability of it being found at different locations. The goal is to determine the whole quantum state, but the particle is only found at one location when a measurement is performed. This new information will then update the belief, boosting the probability around that location.<\/p>\n

Deriving a quantum Bayes\u2019 rule<\/p>\n

The team derived their quantum Bayes\u2019 rule by maximizing the fidelity between two objects that represent the forward and the reverse process, in analogy with a classical joint probability distribution. Maximizing fidelity is equivalent to minimizing change. They found in some cases their equations matched the Petz recovery map, which was proposed by D\u00e9nes Petz in the 1980s and was later identified as one of the most likely candidates for the quantum Bayes\u2019 rule based just on its properties.<\/p>\n

\u201cThis is the first time we have derived it from a higher principle, which could be a validation for using the Petz map,\u201d said Prof Scarani. The Petz map has potential applications in quantum computing for tasks such as quantum error correction and machine learning. The team plans to explore whether applying the minimum change principle to other quantum measures might reveal other solutions.<\/p>\n

Reference: \u201cQuantum Bayes\u2019 Rule and Petz Transpose Map from the Minimum Change Principle\u201d by Ge Bai, Francesco Buscemi and Valerio Scarani, 28 August 2025, Physical Review Letters.
DOI: 10.1103\/5n4p-bxhm<\/a><\/p>\n

Never miss a breakthrough: Join the SciTechDaily newsletter.<\/a><\/b><\/p>\n","protected":false},"excerpt":{"rendered":"Physicists have derived a quantum version of Bayes\u2019 rule, revealing how beliefs and probabilities update in the quantum…\n","protected":false},"author":2,"featured_media":433191,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[3690,128028,3824,74,147226,11112,70,16,15],"class_list":{"0":"post-433190","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-machine-learning","9":"tag-mathematics","10":"tag-national-university-of-singapore","11":"tag-physics","12":"tag-probability","13":"tag-quantum-physics","14":"tag-science","15":"tag-uk","16":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/115224340603755451","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/433190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=433190"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/433190\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/433191"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=433190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=433190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=433190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}