How likely you think something is likely to happen that you already believe in the situation. This simple idea forms the basis of the rule of twenty -two, which is a mathematical approach to calculate the possibilities offered in 1763. Now, an international group of scientists has shown how Base’s rule can also apply to the quantum circle.
“I would say that this is a breakthrough in mathematics physics,” said Professor Valerio Scarani, Deputy Director and Principal Investigator of the Center for Quantum Technologies, and team member. His co -authors at work published on 28 August 2025 Physical review posts Assistant Professor GG Bai at Hong Kong University of Science and Technology in China, and Professor Francisco at Nagoya University in Japan.
“The rule of twenty -two has been helping us to make smart estimates for 250 years. Now we have taught him some quantum plans.”
Although other researchers had previously suggested quantum versions of the twenty -two rule, the team is the first to achieve a real quantum twenty -two rules based on the basic physical principle.
Conditional likely
The rule of twenty -two takes its name from Thomas Base, which describes its methodology to calculate the conditional possibilities in an article in “solving a problem in the theory of possibilities.”
Imagine someone who performs a positive test for the flu. They may already be suspected of the disease, but this new result changes the diagnosis about their conditions. The rule of twenty -two provides a systematic way to update this belief, with the possibility of testing the test as well as the previous assumptions of the person.
This rule presents the possibilities as a belief rather than absolute facts. This interpretation has given rise to a debate among statistics, some people have argued that the possibility should represent the objective frequency rather than a sophisticated trust. Nevertheless, when uncertainty and belief play a role, the rules of twenty -two are widely recognized as a rational framework for decision -making. It supports countless applications from medical testing and weather forecasts to data science and machine learning.
The principle of minimal change
When calculating the possibilities with the principle of twenty -two, the minimum change principle is complied with. According to mathematics, the principle of minimal change reduces the distance between the common and the latest potential distribution of the latest and the latest faith. Interestingly, it is believed that for any new information, beliefs are updated in a smaller way that is compatible with new facts. For example, in the case of a flu test, a negative test does not mean that the person is healthy, but rather that they are less likely to have a flu.
In his work, Professor Scarani, who is also from the NUS Department of Physics, Assistant Professor Bai, and Professor Busseemi started with quantum analog for the minimum change principle. They changed the amount of change in terms of quantum loyalty, which is a measure of closeness among the quantum states.
Researchers have always thought that the rule of quantum twenty -two should be available because quantum states explain the possibilities. For example, the quantum condition of a particle provides the possibility of being found in different locations. The purpose is to determine the entire quantum state, but the particle is found only in one place when the measurement is taken. After that, this new information will promote the possibility of this location.
The team resembled the classic joint potential distribution, maximizing loyalty between the two items and gaining the principle of quantum twenty -two. The maximum sincere change is equivalent to minimizing. In some cases, he found his equality with the PET Z Recovery Map, which was suggested by Dennis Petts in the 1980s, and was later identified as a potential candidate for quantum twenty -two rules based on his characteristics.
“This is the first time we have derived it from a high principle, which can be verified to use the PET Z map,” said Professor Scarani. There are potential applications in quantum computing in PETZ maps such as quantum error correction and machine learning. The team has intended to discover whether the minimum change principle to other quantum measures can lead to other solutions.
