## ローマ第Ⅱ大学 Luigi Accardi 教授の講演会

## のご案内

## ローマ第Ⅱ大学 Luigi Accardi 教授の講演会のご案内

講師：Luigi Accardi 教授

ローマ第Ⅱ大学

日時：令和 6年 2月 27日(火) および 令和 6年 2月 29日(木)

両日 15:00 ～ 16:30

場所：名城大学天白キャンパス共通講義棟東 E-403 室

題目： 2月 27日(火)

The Viterbi algorithm and its application in Hidden Markov Processes

( joint work with Soueidy El Gheteb, Yun Gang Lu, Abdessatar Souissi)

2月 29日(木)

Extensions of quantum mechanics canonically associated to classical probability

要旨：2月 27日(火)

Hidden Markov processes (HMP) (also called Hidden Markov models (HMM)) are

a variant of usual Markov processes which turned out to be extremely successful in a

large number of applications of different type. Recently it has been proved that this

class of processes admits a natural quantum extension and that, from restrictions of

quantum HMP to abelian sub–algebras, one obtains new families of classical processes

with non–trivial potential applications. Many of the results discussed are new also in

the classical case.

2月 29日(木)

Since the first steps of quantum probability (QP) in the years 1970s,

it was a folklore statement that QP is a generalization of classical probability (CP).

Developments over the last 25 years have shown that this statement must be

completely overturned, namely: the whole quantum theory (QT) can be deduced

from the combination of CP with the classical theory of orthogonal polynomials (OP).

The importance of the new point of view does not lie so much in the above–

mentioned deduction, but in the fact that, in this deduction, the known quantum

theory appears as a very special case, corresponding to some specific classical

probabilistic requirements of a much broader deductive theory, which allows to

take into account other, often more realistic, probabilistic requirements.

In other words, for the first time in over 100 years, the mathematical apparatus of

QT appears in the perspective of a natural deduction and not as a strange, singular

theory justified a posteriori by its enormous empirical success, but totally mysterious

in its origins and meaning.

The fall–out of this new point of view, both for QT and for CP has already been

very large, but this is only the beginning and it is not hazardous to expect that, in

the near future, both these disciplines will undergo a radical conceptual and technical

innovation.