## 2014年05月19日ブシェーミ フランチェスコ 准教授（計算機数理科学専攻）2014/4/1着任

Any kind of information processing (acquisition, compression, transmission, deletion) ultimately amounts to processing actual physical systems. Consequently, **it is the laws of physics that pose the ultimate limits in information processing**.

My research activity is about **understanding how information behaves at the quantum scale**. I am therefore interested in any aspect of __fundamental quantum theory__ (in particular, quantum measurement theory, quantum decoherence, quantum entanglement and non-locality), __quantum information theory__ (finite-length and asymptotic coding theorems for general quantum resources), __quantum statistics__ (quantum game theory and quantum statistical experiments), and __quantum thermodynamics__ (information/energy balance in quantum processes).

*Quantum Measurement Theory*

At the basis of any information-processing task relies the notion of information extraction, e.g., readout. The mathematical structure needed to describe such a task is provided, as showed by Masanao Ozawa in full generality, by the notion of "quantum instruments." Any noisy process, evolution, encoding and decoding operation can be conveniently modeled as a specific quantum instrument. This is the reason why the study of quantum instruments and quantum measurement processes enjoys a privileged position within the field of quantum information theory. A central feature of quantum theory is that information extraction cannot be done without disturbing the measured system. This phenomenon, manifesting itself in a variety of forms and situations, is usually named the **Heisenberg Uncertainty Principle**. Within this area, I collaborate with Masanao Ozawa to understand how the uncertainty principle can be formulated within an information-theoretic framework. This research topic has implications in the emerging field of quantum technologies, where the design of accurate, though delicate, measuring apparatuses is of crucial importance.

*Quantum Information Theory*

Following Claude Shannon, information theory can be considered as that body of mathematical works characterizing the ultimate performance limits of various information processing tasks (like source coding, noisy channel coding, etc.). Typically, such rates are computed in the limit of asymptotically many instances of the same information theoretical setting, thought of as identically and independently repeated an infinite number of times (from which the idea of block-coding invented by Shannon has been a major break-through). One of the biggest successes of quantum information theory has been to generalize many of these theorems to the case in which the underlying algebra is non-commutative. This field of research is usually called **Quantum Shannon Theory**. However, in order to assess the performance of real-world information processing tasks, it is important to characterize them when the unphysical assumptions of identical, independent, and infinite repetitions are lifted. In classical information theory, new tools were developed to deal with such a generalized scenario, namely, the **Information Spectrum Approach** and the **Single-Shot Approach**. Recently, these tools have been extended to quantum information theory. Part of my research is devoted to the application of these tools in quantum information theory, especially to the interconversion of entangled quantum resources.

*Quantum Statistics*

The task in which an experimenter tries to learn about an unknown physical system can be nicely formalized as a statistical estimation task or a **statistical decision problem**. The mathematical structures needed to describe such situation in classical statistics are called "statistical models." An important subject in classical statistics, with implications also in the field of the statistical design of experiments, is the **comparison of statistical models **in terms of their information value in statistical decision problems. At present, I am actively working to extend the concepts of statistical model comparison to the quantum setting, where probability measures are replaced by density operators acting on a Hilbert space.

*Career*

I received the PhD in Theoretical Physics from the University of Pavia in 2006. From 2006 to 2008, I was Researcher at the Quantum Computation and Information ERATO-SORST Project, JST, Tokyo. From 2008 to 2009, I was Research Associate at the Statistical Laboratory of the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK. From 2009 to 2014, I was Designated (Tenure-Track) Associate Professor at the Institute for Advanced Research, Nagoya University. From 2014, I am Associate Professor at the Department of Computer Science and Mathematical Informatics of the Graduate School of Information Science, Nagoya University.

*Selected Publications*

F. Buscemi, M. J. W. Hall, M. Ozawa, and M. M. Wilde, *Noise and disturbance in quantum measurements: an information-theoretic approach*. Physical Review Letters, vol. 112, 050401 (2014).

F. Buscemi, *All entangled states are nonlocal*. Physical Review Letters, vol. 108, 200401 (2012).

F. Buscemi, *Comparison of quantum statistical models: equivalent conditions for sufficiency*. Communications in Mathematical Physics, vol. 310, no. 3, pp. 625-647 (2012).

F. Buscemi and N. Datta, *The quantum capacity of channels with arbitrarily correlated noise*. IEEE Transactions on Information Theory, vol. 56, no. 3, 1447 (2010).

F. Buscemi, M. Hayashi, and M. Horodecki, *Global information balance in quantum measurements*. Physical Review Letters, vol. 100, 210504 (2008).

F. Buscemi, *Channel correction via quantum erasure*. Physical Review Letters, vol. 99, 180501 (2007).

F. Buscemi, G. M. D'Ariano, M. Keyl, P. Perinotti, and R.F. Werner, *Clean positive operator valued measures*. Journal of Mathematical Physics, vol. 46, 082109 (2005).