Masanori Ohya

Tokyo University of Science | TUS · Department of Information Sciences

In this study, we discuss a non-Kolmogorovness of the optical illusion in the human visual perception. We show subjects the ambiguous figure of "Schröeder stair", which has two different meanings [1]. We prepare 11 pictures which are inclined by different angles. The tendency to answer "left side is front" depends on the order of showing those pict...

In 2000, Ohya et al. proposed a quantum algorithm with the amplification process of success probability, so-called chaos amplifier. They defined the process based on the logistic map, and its chaos behaviour amplifies the probability very fast. In this paper, we construct the chaos amplifier using a lifting map, a master equation and a partial trac...

Optical illusion is one of the fundamental phenomena depending on experimental contexts (settings). Figure 1 is called a Schröder stair (Schröder 1858). We can see stairs in the middle of the figure, and it has two possible ways of observing it: One way is that “the left part (L) is front and the right part (R) is back,” and another way is its conv...

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond t...

Recently a novel quantum information formalism - quantum adaptive dynamics - was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantu...

We compare the contextual probabilistic structures of the seminal two-slit experiment (quantum interference experiment), the system of three interacting bodies and Escherichia coli lactose-glucose metabolism. We show that they have the same non-Kolmogorov probabilistic structure resulting from multi-contextuality. There are plenty of statistical da...

The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. More...

This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cell...

In this chapter, we briefly introduce the basic concept of molecular biology and also biological information processing in general. As a detailed example of the information processing phenomena (signal recognition, transformation, and biological response) in a living system, we explain the diauxie (two phase) growth of Escherichia coli in glucose a...

In this chapter we present briefly the basic notions of classical and quantum theories of probability and information. This chapter is especially important for biologists, psychologists, experts in cognition, and sociologists who were not trained in quantum theory (but even classical theory is presented in a simple manner). We start with the presen...

This chapter is devoted to a model of the epigenetic cellular evolution based on the mathematical formalism of open quantum systems. We emphasize that, although in this book we restrict our QL-modeling to the epigenetic evolution, it is clear that the structure of the model allows it to be extended to describe evolution of biological organisms in g...

In this chapter the formalism of quantum probability and quantum information theory (in its generalized form based on theory of lifting) is applied to construct the QL-representations for cognitive processes, especially decision making in games of the prisoner’s dilemma type. Our modeling is based on the results of extended studies in the domain of...

In this chapter we discuss the possibility to apply the quantum formalism to model biological evolution, especially at the cellular level—genetic and epigenetic evolutions. We start with an extended historical introduction which can be useful for non-biologists, physicists, mathematicians, psychologists, sociologists. In particular, detailed compar...

In this chapter, we will discuss the non-Kolmogorov probability theory. Our aim is to explain where and why the usual probability theory is broken. The basic example from quantum physics is presented in very detail including the corresponding illustrations. This is the two slit experiment demonstrating interference for quantum systems. Further, we...

In this chapter, we present examples of the nonclassical probabilistic behavior of concrete microbiological systems: cells and proteins. The experimental data exhibit the interference effect which is similar to interference of probabilities observed in quantum physics. Finally, we apply the formalism of quantum adaptive dynamics to model nonclassic...

Since the classical formula of total probability is violated for data from both QM and cognitive psychology and the former has developed the advanced mathematical apparatus for the study of the interference effect, it is natural to apply this apparatus to describe statistical data of the latter. However, there is one pitfall; one problem has to be...

In this chapter, we briefly discuss the main foundational problems of quantum mechanics, especially the problem of hidden variables—variables which might provide finer description of quantum phenomena than given by quantum states.

We discuss foundational issues of quantum information biology (QIB) -- one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional...

This book examines information processing performed by bio-systems at all scales: from genomes, cells and proteins to cognitive and even social systems. It introduces a theoretical/conceptual principle based on quantum information and non-Kolmogorov probability theory to explain information processing phenomena in biology as a whole. The book begin...

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, $(t_1, t_2), (t_2, t_3),...

In this paper, we discuss a coupling system constructed from the logisticmap and the tent map. We also discuss an approach for maximizing the entropy of the system.

Recently, it has been reported that conventional probability law can be violated in the context dependent phenomena which are 'adaptive' to the environment or experimental settings. Also, it has been discussed that non-Kolmogorov probability, e.g. quantum probability, is available for modeling such a context dependent phenomenon. In this study, we...

Ohya and Volovich proposed the polynomial time quantum algorithm to solve SAT problem which is one of NP-complete problems. This algorithm contains effective amplification process, so called a Chaos Amplifie, based on classical Chaotic dynamics. Recently we described this process by the GKSL master equation on two qubits system. In this talk, we in...

We develop a quantum-like (QL) model of cellular evolution based on the theory of open quantum systems and entanglement between epigenetic markers in a cell. This approach is applied to modeling of epigenetic evolution of cellular populations. We point out that recently experimental genetics discovered numerous phenomena of cellular evolution adapt...

Recently, various examples of non-Kolmogorovness in contextual dependent phenomena have been reported. In this study, we introduce non-Kolmogorovness in the measurement of depth inversion for the figure of Schröder’s stair. Also we propose a model of the depth inversion, based on a non-Kolmogorovian probability theory which is called adaptive dynam...

The well known quantum algorithm for search problem is Grover’s one. However, its computational complexity is not a polynomial in the input. In this study, we propose a polynomial time quantum algorithm for it based on quantum binary search and an amplification process. This process can be written as a quantum Turing machine form, a so called gener...

There exist several criteria to describe the chaotic behaviour of a dynamical system. In this paper, we discuss the relations among three criteria: Entropic Chaos Degree, Kolmogorov-Shinai entropy, and Lyapunov exponent. Moreover, the problems of their computation are discussed.

We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formal...

Several scientific and technical problems can be described by a stochastic partial differential equation. The solution of the equation could be considered as the limit of a suitable discrete particle model. The existence of such a kind of approximation was discussed in [the first author and and M. Schmidt, Serdica 13, 396–402 (1987; Zbl 0641.60070)...

We will show the necessary and sufficient condition of separability for a sub-class of circulant states in the ℂ 3 ⊗ℂ 3 system. This sub-class includes the models proposed by several authors as special cases. Moreover, it will be proved that our separability condition equals to the failure condition of quasi-distillation of entanglement.

The tumor-suppressor gene TP53 mutations are very diverse in the central region encoding the DNA-binding domain. It has not been clear whether the prognostic significance for survival in breast cancer patients is the same for all types of mutations. Are there specific types of mutations carrying a worse prognosis? In order to understand the correla...

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quan...

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

This research is related to the problem of “irrational decision making or inference” that have been discussed in cognitive psychology. There are some experimental studies, and these statistical dat ...

Using EEG measurements one gets information on the densities of excited neurons located in the regions of the brain. Up to now there exist different hypothesises concerning the distribution of the random outcomes of EEG measurements. Using classical models for describing brain activities it turned out to be difficult to explain the observed propert...

We present the general formalism of decision making which is based on the theory of open quantum systems. A person (decision maker), say Alice, is considered as a quantum-like system, i.e., a syste ...

Based on classical models of brain activities it seems to be difficult to explain the internal noise related to EEG-measurements. In this paper using a quantum model of the recognition process we consider the asymptotic behaviour of that internal noise.

We apply theory of open quantum systems to modeling of epigenetic evolution. This is an attempt to unify Darwinian and Lamarckian viewpoints on evolution on the basis of a quantum-like model. The state of uncertainty of cell's epigenome is resolved to a stable and inherited epigenetic configuration. This process of evolution and stabilization is de...

Considering models based on classical probability theory, states of signals in the brain should be identified with probability distributions of certain random point fields representing the configuration of excited neurons. Then the outcomes of EEG-measurements can be considered as random variables being certain functions of that random point field....

In this paper we apply the quantum-like (QL) approach to microbiology to present an operational description of the complex process of diauxie in Escherichia coli. We take as guaranteed that dynamics in cells is adaptive, i.e., it depends crucially on the microbiological context. This very general assumption is sufficient to appeal to quantum and mo...

Recently it is pointed out that there exists the experimental data in Escherichia coli's metabolism which violate the law of total probability in classical probability. In this report, we propose a model which describes such phenomenon based on adaptive dynamics.

In this paper we develop a general quantum-like representation of decision making. Here quantum-like representation is based on linear algebra, the von Neumann-Lüders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. Our approach generalizes in a natural way the classic...

There exist several phenomena (systems) breaking the classical probability laws. In this report, we present a new mathematical formula to compute the probability in those context dependent systems by using the concepts of the adaptive dynamics and the lifting.

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...

In this paper we develop a general quantum-like model of decision making. Here updating of probability is based on linear algebra, the von Neumann–Lüders projection postulate, Born’s rule, and the quantum representation of the state space of a composite system by the tensor product. This quantum-like model generalizes the classical Bayesian inferen...

A new scheme for quantum teleportation is presented, in which teleportation channel from Alice to Bob is always linear and complete (total) teleportation can occur even when an entangled state between Alice and Bob is not maximal.

We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machine (GQTM) contains not only unitary computation process but also quantum measurement and dissipative process. Moreover, we discovered...

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the “rational strategy” provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can...

In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6,...

Recently, we proposed a new method to compute probabilities which do not satisfy basic law in classical probability theory. In this note, we analyze glucose effect in Escherichia coli's growth with the method, and we show an invariant quantity which Escherichia coli has.

In this paper, we constmct a teleportation model with nonmaximal entangled state. This model, called the m-level teleportation, is discussed on the basis of the Kossakowski and Ohya teleportation scheme. For this study, we define a generalized Bell state in terms of Latn square, by which we derive a general form of appropriate nonmaximal entangled...

We review the quantum chaos algorithm solving the NP-complete problems in polynomial time. This work has been done in the series of papers with Professor Igor Volovich for nearly ten years.

We present a brief review of the scientific work and achievements of Igor V. Volovich on the occasion of his 65th birthday.

In modern brain research, an internal noise caused by the memory is represented by the output of EEG-measurements. However, based on classical models specialists in EEG-mapping cannot explain the observed properties of the internal noise. In this paper, using quantum models, we consider the asymptotic behaviour of the internal noise caused by the m...

We present quantum mechanics (QM) as theory of special classical random signals. On one hand, this approach provides a possibility to go beyond conventional QM: to create a finer description of micro processes than given by the QM-formalism. In fact, we present a model with hidden variables of the wave-type. On the other hand, our approach establis...

Entangled Markov chains (EMC) were so baptized on the basis of the conjecture that they provide examples of states, on infinite tensor products of matrix algebras, which are in some sense “entangled”. We introduce the notion of multiple (or “many-body”) entanglement and extend the two-body criterion of entanglement obtained by M. Ohya and T. Matsuo...

A dynamical entropy for not only shift but also completely positive (CP) map is defined by generalizing the AOW entropy1 defined through quantum Markov chain and AF entropy defined by a finite operational partition. Our dynamical entropy is numerically computed for several models.

Quantum entanglements, describing truly quantum couplings, are studied and classified for discrete compound states. We show that classical-quantum correspondences such as quantum encodings can be treated as d-entanglements leading to a special class of separable compound states. The mutual information for the d-compound and for q-compound (entangle...

In the last ISABEL, we showed a high quality sequence alignment method called MTRAP. Although there exists a need for high quality alignment, a treatable alignment software, as typified by ClustalW, is also essential for the analysis estimating the function of gene or to seek mechanism of molecular interactions. In this paper, we develop a new trea...

We study the correlations of classical and quantum systems from the information theoretical points of view. We analyze a simple measure of correlations based on entropy (such measure was already investigated as the degree of entanglement by Belavkin, Matsuoka and Ohya). Contrary to naive expectation, it is shown that separable state might possesses...

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (repres...

We present the quantum-like paradigm for biology, cognitive psychology, and modeling of brain's functioning. By this paradigm contextuality of biological processes induces violation of laws of classical (Kolmogorovian) probability, starting with the fundamental law of total probability. New nonclassical models have to be used for mathematical model...

We propose a double blinding-attack on entangled-based quantum key distribution protocols. The principle of the attack is the same as in existing blinding attack except that instead of blinding the detectors on one side only, Eve is blinding the detectors of both Alice and Bob. In the BBM92 protocol, the attack allows Eve to get a full knowledge of...

In this note we illustrate on a few examples of cells and proteins behavior that microscopic biological systems can exhibit a complex probabilistic behavior which cannot be described by classical probabilistic dynamics. These examples support authors conjecture that behavior of microscopic biological systems can be described by quantum-like models,...

I first met Professor Ingarden nearly 30 years ago. Since then, he visited my University in Tokyo many times and I also often visited him in Toruń. In this paper, I will recall our scientific collaboration and I will review what I have done under his advice. Moreover, I will report on my recent work with A. Khrennikov on formulating a new probabili...

There exist several phenomena (systems) breaking the classical probability laws. Such systems are contextual dependent adaptive systems. In this paper, we present a new mathematical formula to compute the probability in those systems by using the concepts of the adaptive dynamics and quantum information theory -- quantum channels and the lifting. T...

We have studied a quantum algorithm for several years, and developed some applications for difficult problems, NPC problems and NP intermidiate problems. In order to discuss the computational complexity of quantum algorithm, we defined a generalized quantum Turing machine using a density operator on a Hilbert space and quantum channels on it. Since...

A lifting is a map from the state of a system to that of a compound system, which was introduced in Accardi and Ohya (Appl. Math. Optim. 39:33–59, 1999). The lifting can be applied to various physical processes. In this paper, we defined a quantum mutual entropy by the lifting. The usual quantum mutual entropy satisfies the Shannon inequality (Ohy...

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10...

Recently, applications of quantum mechanics to coginitive psychology have been discussed, see [1]–[11]. It was known that statistical data obtained in some experiments of cognitive psychology cannot be described by classical probability model (Kolmogorov’s model) [12]–[15]. Quantum probability is one of the most advanced mathematical models for non...

I will discuss the cocept of Adaptive dynamics (AD for short) and mention how it is used in quantum information, chaos dynamics, bio‐sciences and others.

It has been considered that a maximal entangled state is needed for complete quantum teleportation. However, Kossakowski and Ohya proposed a scheme of complete teleportation for nonmaximal entangled state [1]. Basing on their scheme, we proposed a teleportation model of 2-level state with a non-maximal entangled state [2]. In the present study, we...

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using...

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 (1992), Croson (1999), Hofstader (1983, 19...

In elaborating on the multiple-photon absorption attack on Ekert protocol proposed in arXiv:1011.4740, we show that it can be used in other entanglement-based protocols, in particular the BBM92 protocol. In this attack, the eavesdropper (Eve) is assumed to be in control of the source, and she sends pulses correlated in polarization (but not entangl...

We analyze the procedure of lifting in classical stochastic and quantum systems. It enables one to `lift' a state of a system into a state of `system+reservoir'. This procedure is important both in quantum information theory and the theory of open systems. We illustrate the general theory of liftings by a particular class related to so called circu...

In quantum communication theory, one looks for the most efficient way to code information and construct a physical device (channel) in order to send information as completely as possible. There “quantum” means that we code information by quantum states and send it through a properly designed quantum device. If one can send any quantum state from an...

In this chapter we will consider a new approach to quantum computations. We shall discuss an algorithm introduced by Ohya and Volovich which can solve the NP-complete satisfiability (SAT) problem in polynomial time. The algorithm goes beyond the quantum Turing machine paradigm.

In this chapter, we discuss the basics in the classical probability theory. Probability theory is based on measure theory, so that we start by reviewing measure theory.

We discuss in this chapter the following topics in quantum information: (1) the channel capacity for quantum communication processes by applying the quantum mutual entropy introduced in Chap. 7, (2) formulations of quantum analogues of McMillan’s theorem and coding type theorem for entanglement transmission.

In this chapter, some basic notions of quantum field theory will be exposed and properties of entanglement and locality will be considered again in this new context. The relativistic corrections to the EPR–Bell type correlation functions for entangled states of the Dirac particles will be computed and it will be shown that the spatially depending c...

This chapter is devoted to miscellaneous topics related to quantum information and quantum probability. They haven’t been either completed or used much for quantum information, yet, but they will be important for the future development in these fields. Topics discussed in this chapter are more or less conceptual, so that we will not always provide...

In this chapter basic notions of quantum information will be considered. A channel is a mapping of an input state to an output state. The amount of information transmitted from input to output is described by the mutual entropy.

In this chapter, we briefly review the basic facts of the classical information communication processes. The fundamental aspects of information theory according to Shannon (Bell Syst. Tech. J. 27:379–423, 623–656, 1948) are composed of the following concepts: message; entropy describing the amount of information; communication channel, mutual entro...

In this chapter, the discrete quantum Fourier transform, the Deutsch–Jozsa algorithm for balanced functions, and the Grover algorithm for database search are exposed.

There exist various approaches to study chaotic behavior of systems by means of several concepts such as entropy, complexity, chaos, fractal, stochasticity. In 1991, the term Information Dynamics (ID) was proposed by Ohya with the aim of finding a common framework of treating such chaotic behaviors of different systems altogether. That is, ID is an...

In this chapter, certain experimental realizations of quantum information schemes are briefly discussed. Some nanosystems used for experimental implementation of quantum computation such as quantum dots, ion traps, and nuclear magnetic resonance are considered. Parametric down-conversion for producing entangled photons is described. Full expositio...