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The operational structure of quantum couplings and entangle-ments is studied and classified for semifinite von Neumann algebras. We show that the classical-quantum correspondences such as quantum encodings can be treated as diagonal semi-classical (d-) couplings, and the entanglements characterized by truly quantum (q-) couplings, can be regarded as truly… (More)
In complexity theory, there exists a famous unsolved problem whether NP can be P or not. In this paper, we discuss this aspect in SAT (sat-isfiability) problem, and it is shown that the SAT can be solved in plynomial time by means of quantum algorithm.
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm which is a combination of the ordinary quantum algorithm with a chaotic dynamical system. We consider the satisfiability… (More)
We interpret the Leggett-Garg (LG) inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts. In the original version of the inequality these contexts have the temporal nature and they are given by three pairs of instances of time, (t1, t2), (t2, t3), (t3, t4),… (More)
We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes' inequality.
We proceed towards an application of the mathematical formalism of quantum mechanics to cognitive psychology — the problem of decision-making in games of the Prisoners Dilemma type. These games were used as tests of rationality of players. Experiments performed in cognitive psychology by Shafir and Tversky [1, 2], Croson , Hofstader [4, 5] demonstrated… (More)
We developed a quantum-like model describing the gene regulation of glucose/lactose metabolism in a bacterium, Escherichia coli. Our quantum-like model can be considered as a kind of the operational formalism for microbiology and genetics. Instead of trying to describe processes in a cell in the very detail, we propose a formal operator description. Such a… (More)