On an Effectiveness of Quantum Mini-Max Formula in Quantum Communication

蒼一朗 藤田, 正雄 大崎

Here we give the result of the classical detection theory, which satisfies the mini-max condition for the ternary coherent signal. In detail, a priori probabilities of the signal are derived from the necessary and sufficient conditions of the mini-max strategy and compared with those obtained by the quantum detection theory.

Alexander Semenovich Holevo

Takahiro Kajisa

The Boltzmann’s formula, formally known as S = log W, provides a basic concept of a relation between the logarithmic number of micro states log W and the thermodynamic entropy S. In this paper, we prove the Boltzmann’s formula in quantum unbounded lattice systems that includes not only the quantum anharmonic oscillator but also the Bose–Hubbard type model with negative interactions. Our approach is based on a particle number cut-off method, mini-max theory, and convex analysis. In particular, the cut-off method, nurtured in my previous work on classical non-compact spin systems [T. Kajisa. Rev. Math. Phys. 36(08), 2450021 (2024)] is well harmonized with the non-commutative approximation method developed in [Stachura et al., J. Math. Phys. 61(11), 113303 (2020)]. Finally, we present how to relax the assumption of the negativity of interactions.

Debarka Mukhopadhyay, Siddhartha Bhattacharyya, Jan Platoš +2 more

Masahito Hayashi

Kentaro Kato, Masao Osaki, Tomohiro Suzuki +2 more