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Takayuki Miyadera

Publications and source records attributed to Takayuki Miyadera.

At least 55 records · Page 3Linked to original sources
arXiv2009

Optimal State Discrimination in General Probabilistic Theories

We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles (which we call a {\it Helstrom family of ensembles}) with the problem, we provide a geometrical method to find an optimal measurement for state discrimination by means of Bayesian strategy. We illustrate our method in 2-level quantum systems and in a probabilistic model with square-state space to reproduce e.g., the optimal success probabilities for binary state discrimination and $N$ numbers of symmetric quantum states. The existences of families of ensembles in binary cases are shown both in classical and quantum theories in any generic cases.

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arXiv2009

Quantum Kolmogorov Complexity and Quantum Key Distribution

We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol in the light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The program length necessary to describe an object, Kolmogorov complexity, plays the most fundamental role in the theory. In the context of algorithmic information theory, we formulate a security criterion for the quantum key distribution by using the quantum Kolmogorov complexity that was recently defined by Vitányi. We show that a simple BB84 protocol indeed distribute a binary sequence between Alice and Bob that looks almost random for Eve with a probability exponentially close to 1.

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arXiv2008

Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures

A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive operator valued measures to be simultaneously measurable is obtained.

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arXiv2007

Generalized Landau-Pollak Uncertainty Relation

The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of positive operator valued measures. A nontrivial but slightly weak inequality that can treat an arbitrary number of positive operator valued measures is also presented.

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arXiv2007

Information-Disturbance theorem and Uncertainty Relation

It has been shown that Information-Disturbance theorem can play an important role in security proof of quantum cryptography. The theorem is by itself interesting since it can be regarded as an information theoretic version of uncertainty principle. It, however, has been able to treat restricted situations. In this paper, the restriction on the source is abandoned, and a general information-disturbance theorem is obtained. The theorem relates information gain by Eve with information gain by Bob.

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arXiv2006

Strength of interaction for information distribution

Let us consider two quantum systems: system A and system B. Suppose that a classical information is encoded to quantum states of the system A and we distribute this information to both systems by making them interact with each other. We show that it is impossible to achieve this goal perfectly if the strength of interaction between the quantum systems is smaller than a quantity that is determined by noncommutativity between a Hamiltonian of the system A and the states (density operators) used for the information encoding. It is a consequence of a generalized Winger-Araki-Yanase theorem which enables us to treat conserved quantities other than additive ones.

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arXiv2006

Wigner-Araki-Yanase theorem on Distinguishability

The presence of an additive conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, the perfect repeatability and the distinguishability on the apparatus cannot be attained simultaneously. Instead of the repeatability, in this paper, the distinguishability on both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. The inequality shows that the perfect distinguishability of both systems cannot be attained simultaneously.

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arXiv2006

Entangled Markov Chains generated by Symmetric Channels

A notion of entangled Markov chain was introduced by Accardi and Fidaleo in the context of quantum random walk. They proved that, in the finite dimensional case, the corresponding states have vanishing entropy density, but they did not prove that they are entangled. In the present note this entropy result is extended to the infinite dimensional case under the assumption of finite speed of hopping. Then the entanglement problem is discussed for spin 1/2, entangled Markov chains generated by a binary symmetric channel with hopping probability $1-q$. The von Neumann entropy of these states, restricted on a sublattice is explicitly calculated and shown to be independent of the size of the sublattice. This is a new, purely quantum, phenomenon. Finally the entanglement property between the sublattices ${\cal A}(\{0,1,...,N\})$ and ${\cal A}(\{N+1\})$ is investigated using the PPT criterium. It turns out that, for $q\neq 0,1,{1/2}$ the states are non separable, thus truly entangled, while for $q=0,1,{1/2}$, they are separable.

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arXiv2005

Quantum Dynamical Entropy of Spin Systems

We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of the state.

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arXiv2004

Slow decay of dynamical correlation functions for nonequilibrium quantum states

A property of dynamical correlation functions for nonequilibrium states is discussed. We consider arbitrary dimensional quantum spin systems with local interaction and translationally invariant states with nonvanishing current over them. A correlation function between local charge and local Hamiltonian at different spacetime points is shown to exhibit slow decay.

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arXiv2004

Coarse-Grained Picture for Controlling Quantum Chaos

We propose a coarse-grained picture to analyze control problems for quantum chaos systems. Using optimal control theory, we first show that almost perfect control is achieved for random matrix systems and a quantum kicked rotor. Second, under the assumption that the controlled dynamics is well described by a Rabi-type oscillaion between unperturbed states, we derive an analytic expression for the optimal field. Finally we numerically confirm that the analytic field can steer an initial state to a target state in random matrix systems.

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arXiv2003

Anomalous quantum states in finite macroscopic systems

We consider finite macroscopic systems, i.e., systems of large but finite degrees of freedom, which we believe are poorly understood as compared with small systems and infinite systems. We focus on pure states that do not have the `cluster property.' Such a pure state is entangled macroscopically, and is quite anomalous in view of many-body physics because it does not approach any pure state in the infinite-size limit. However, we often encounter such anomalous states when studying finite macroscopic systems, such as quantum computers with many qubits and finite systems that will exhibit symmetry breaking in the infinite-size limit. We study stabilities of such anomalous states in general systems. In contrast to the previous works, we obtain general and universal results, by making full use of the locality of the theory. Using the general results, we discuss roles of anomalous states in quantum computers, and the mechanism of emergence of a classical world from quantum theory.

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arXiv2003

On energy-momentum spectrum of stationary states with nonvanishing current on 1-d lattice systems

On one-dimensional two-way infinite quantum lattice system, a property of translationally invariant stationary states with nonvanishing current expectation is investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show that spectrum of the unitary operators, energy-momentum spectrum with respect to the state, has a singularity at the origin.

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arXiv2003

On Halting Process of Quantum Turing Machine

We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, can not avoid the notion of halting to be probabilistic in Quantum Turing Machine. Our result suggests that halting scheme of Quantum Turing Machine and quantum complexity theory based upon the existing halting scheme sholud be reexamined.

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arXiv2003

Dynamical aspects of quantum entanglement for coupled mapping systems

We investigate how the dynamical production of quantum entanglement for weakly coupled mapping systems is influenced by the chaotic dynamics of the corresponding classical system. We derive a general perturbative formula for the entanglement production rate which is defined by using the linear entropy of the subsystem. This formula predicts that {\it the increment of the strength of chaos does not enhance the production rate of entanglement} when the coupling is weak enough and the subsystems are strongly chaotic. The prediction is confirmed by numerical experiments for coupled kicked tops and rotors. We also discuss the entanglement production using the Husimi representation of the reduced density matrix.

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arXiv2003

Nonequilibrium steady states on 1-d lattice systems and Goldstone theorem

On one-dimensional two-way infinite lattice system, a property of stationary (space-) translationally invariant states with nonvanishing current expectations are investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show, by applying Goldstone-theorem-like argument,that spectrum of the unitary operators, energy-momentum spectrum with respect to the state, has a singularity at the origin.

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arXiv2002

Stability of quantum states of finite macroscopic systems

We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which describes the strength of spatial correlations of fluctuations of local observables, and to fluctuations of additive operators. The present theory has many applications, among which we discuss the mechanism of phase transitions in finite systems and quantum computers with a huge number of qubits.

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