# Is it possible to use Bayesian method in improving the measuring conditions and accuracy of an electron's (or photon) momentum and position?

for you who need a definition for what a "Bayesian method" is, and as per wiki's easy definition. it's a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".

i would like to hint that me using the term "Bayesian" does not mean literal implication to this definition as in the realm of classical measurements, but rather, the most Bayesian way to measure in a quantum world. in other words, As Bayesian as a quantum measurement method can get

the question says it all really, but those who are interested in details i might want to say that my question does not aim to measure electron's momentum and position simultaneously, but rather improve the conditions by some sort of a Bayesian method. was there any attempt to research that? if so is there any papers that discusses that?

more on that, can it be really applicable on a single electron measurement, without the need to make a conclusion based on studying, say, a beam of electrons or so.

Also, what will be the upper limit on this Bayesian process?

it's worth noting that the tag section does not let me tag anything related to Bayes or Bayes theorem.

I don't think a Baysian method can help with quantum mechanics because the Shrödinger uncertainty relation is physical, if you know observable $$A$$ your state collapses to it's eigenfunction and you know about $$B$$ with an uncertainty dictated by the relation. A great example of using this is in squeezed coherent states where you exploit this relation to get a state with your desired properties.