**September 15, 2023. Friday. 3PM.**

**Room**: TG23 (Town Hall Building)

**Speaker: Takashi Matsuoka** (Suwa University of Science, Japan)

**Title: **Compound States via Quantum Conditionality and Quantum Mutual Entropy

**Abstract: **It will be shown that quantum state on composite system may be represented by a composition of two types of complete positive maps, one is called by standard entanglement and another one is called by quantum conditionality, and such construction can be regarded as the quantum analogue of Bayes formula. How are both quantum marginal states in composite system related may be explained via entangling operator. In addition, using this analogical scheme of Bayes formula, we can define the mutual entropy on our compound state, which may be regarded as the measure representing the correlation between two marginal states. In this talk, on the basis of above construction we will discuss a border of classical-quantum correlation in the context of a generalization of information theory from a classical system to a quantum system.It will be shown that quantum state on composite system may be represented by a composition of two types of complete positive maps, one is called by standard entanglement and another one is called by quantum conditionality, and such construction can be regarded as the quantum analogue of Bayes formula. How are both quantum marginal states in composite system related may be explained via entangling operator. In addition, using this analogical scheme of Bayes formula, we can define the mutual entropy on our compound state, which may be regarded as the measure representing the correlation between two marginal states. In this talk, on the basis of above construction we will discuss a border of classical-quantum correlation in the context of a generalization of information theory from a classical system to a quantum system.

**Bio:** Takashi Matsuoka obtained his PhD in 1996 from the Department of Information Science, Tokyo University of Science (TUS). He then spent one year as a postdoctoral fellow at Copernicus University in Poland and as a part-time lecturer at the Tokyo University of Science before obtaining a job at the Department of Management Information at the Tokyo University of Science, Suwa which was a branch of TUS in 2002, where he has maintained his post to the present day. He specialises in quantum information theory, in particular attempting to analyse quantum compond states and quantum entropies using functional analysis and algebraic approaches.

**Online Link for Microsoft Teams: **

Meeting ID: 311 086 929 946

Passcode: 7DpshS