arXiv subjects
Publications and source records attributed to M. Ohya.
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.
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 circulant states.
A detailed characterization of PPT states, both in the Heisenberg and in the Schrödinger picture, is given. Measures of entanglement are defined and discussed in details. Illustrative examples are provided.
A new scheme for quantum teleportation is presented, in which the complete teleportation can be occurred even when an entangled state between Alice and Bob is not maximal.
We study a possible function of brain, in particular, we try to describe several aspects of the process of recognition. In order to understand the fundamental parts of the recognition process, the quantum teleportation scheme seems to be useful. We consider a channel expression of the teleportation process that serves for a simplified description of the recognition process in brain.
The operational structure of quantum couplings and entanglements 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 quantum encodings. The relative entropy of the d-compound and entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the maximum of mutual information over all d-entanglements, and the dimensional entropy, which is achieved at the standard entanglement -- true quantum entanglement, coinciding with a d-entanglement only in the case of pure marginal states. The d- and q- information of a quantum noisy channel are respectively defined via the input d- and q- encodings, and the q-capacity of a quantum noiseless channel is found as the logarithm of the dimensionality of the input algebra. The quantum capacity may double the classical capacity, achieved as the supremum over all d-couplings, or encodings, bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra.
We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.
Quantum baker`s map is a model of chaotic system. We study quantum dynamics for the quantum baker's map. We use the Schack and Caves symbolic description of the quantum baker`s map. We find an exact expression for the expectation value of the time dependent position operator. A relation between quantum and classical trajectories is investigated. Breakdown of the quantum-classical correspondence at the logarithmic timescale is rigorously established.
Recently, it has been known that a quantum entangled state plays an important role in the field ofquantum information theory such as quantum teleportation and quantum computation. The research on quantifying entangled states has been done by several measures. In this letter, we will adopt the method using quantum mutual entropy to measure the degree of entanglement of Jaynes-Cummings model.