Research

Research Motivation

• Not every information processing (including preparation of states and measurements) in quantum theory is always physically permissible under a given system. Thus, characterizing classes of physically permissible information processes and exploring their mathematical structures is vital for realizing quantum devices. I aim to construct a theoretical basis for implementing information processing as ideally as possible using realistic quantum devices constrained by thermodynamic principles.
• Mathematically, quantum theory includes classical theory, and it has various properties that do not appear in classical theory. I would like to characterize them under the framework of dynamical resource theories and quantitatively treat them from a game-theoretic viewpoint.
• Why is the natural world described by quantum mechanics? To answer this question, I am interested in constructing information theory and thermodynamics in operationally admissible probabilistic models called General Probabilistic Theories (GPTs). I am thinking about things like: Are the laws of thermodynamics related to the mathematical structure of physical theory? Can information theory be developed in theories beyond quantum?

Thermodynamics beyond quantum theory

Deriving quantum theory from natural operational axioms is the fundamental problem of quantum theory. General probabilistic theories (in short, GPTs) are frameworks that denote physical theories in fully operational narratives, and this research direction aims to understand what operational or physical assumptions can restrict the model of GPTs so that it becomes quantum theory (see e.g., [1-2]). In particular, I am studying entropy in GPTs because I am interested in the following question: Can we consider thermodynamics beyond quantum theory?

Some previous researchers have proposed several different operational definitions of entropy in GPTs [3-5]. However, they may produce different values while if we apply these definitions to quantum theory, they produce the same entropy, von Neumann entropy.

One can regard von Neumann entropy as the amount of work we need for separating mixed states into eigenstates of it. This thought experiment was originally introduced by von Neumann [6] and he assumed the spectral theorem, which seems to be not an operational property.

Our work, on the other hand, extracted the assumptions that are needed for accomplishing von Neumann's thought experiment and reconstructed it in a fully operational framework. Then we found that it is the second law of thermodynamics, not the spectral theorem that makes entropy unique: Shintaro Minagawa, Hayato Arai, Francesco Buscemi, Von Neumann’s information engine without the spectral theorem, Physical Review Research 4, 033091, (2022).

[1] P. Janotta and H. Hinrichsen, Journal of Physics A: Mathematical and Theoretical 47, 323001 (2014).
[2] M. Plavala, Phys. Rep. 1033, 1 (2023).
[3] H. Barnum, J. Barrett, L. O. Clark, M. Leifer, R. Spekkens, N. Stepanik, A. Wilce, and R. Wilke, New Journal of Physics 12, 033024 (2010).
[4] A. J. Short and S. Wehner, New Journal of Physics 12, 033023 (2010).
[5] G. Kimura, J. Ishiguro, and M. Fukui, Phys. Rev. A 94, 042113 (2016).
[6] J. von Neumann, Mathematical foundations of quantum mechanics, translated from the German edition by ROBERT T. BEYER (Princeton university press, 1955).

Incompatibility of quantum instruments

One of the most important features of quantum theory is incompatibility. In the context of measurement, it is a notion of joint measurability. If we say more general and operationally, when multiple quantum devices (i.e., measurements, channels, and instruments) can be combined into one, then they are "compatible". Otherwise, they are "incompatible" (for the review, see, e.g., [1]).

While the incompatibility of POVM has been well studied so far, recently, some researchers have tried to consider the incompatibility of quantum instruments. There are several different notions on the incompatibility of quantum instruments [2, 3].

Our paper:

Francesco Buscemi, Kodai Kobayashi, Shintaro Minagawa, Paolo Perinotti, Alessandro Tosini, Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication, Quantum 7, 1035 (2023).

characterizes the family of quantum instruments as a programmable quantum channel and constructs free superchannels that do not produce the incompatibililty, discussing those incompatibilities in the framework of resource theories of quantum channels. This unified view of incompatibility by resource theories of quantum channels reveals the relationships between those different notions of incompatibility. Moreover, we give a necessary and sufficient condition for the free superchannels to convert a family of instruments to another one from a game-theoretic viewpoint, providing a way to treat quantum incompatibility quantitatively.

[1] O. Gühne, E. Haapasalo, T. Kraft, J. Pellonpää, and R. Uola, Rev. Mod. Phys. 95, 011003 (2023).
[2] A. Mitra and M. Farkas, Phys. Rev. A 105, 052202, (2022).
[3] G. M. D’Ariano, P. Perinotti, and A. Tosini, J. Phys. A: Math. Theor. 55(39), 394006 (2022).