Hiromichi Ohno

FREE ENERGY DENSITY FOR MEAN FIELD PERTURBATION OF STATES OF A ONE-DIMENSIONAL SPIN CHAIN

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).

QUANTUM MARKOV FIELDS ON GRAPHS

We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on

EXTENDABILITY OF GENERALIZED QUANTUM MARKOV CHAINS ON GAUGE INVARIANT C*-ALGEBRAS

C^*

Unitary equivalent classes of one-dimensional quantum walks

-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.

Maximal rank of extremal marginal tracial states

We prove the extendability of generalized quantum Markov chains on gauge-invariant parts of UHF algebras to Markov chains on ambient UHF algebras.

How to detect a possible correlation from the information of a subsystem in quantum-mechanical systems

This study investigates unitary equivalent classes of one-dimensional quantum walks. We prove that one-dimensional quantum walks are unitary equivalent to quantum walks of Ambainis type and that translation-invariant one-dimensional quantum walks are Szegedy walks. We also present a necessary and sufficient condition for a one-dimensional quantum walk to be a Szegedy walk.

Relation between the dynamics of the reduced purity and correlations

States on the coupled quantum system Mn(C)⊗Mn(C) whose restrictions to each subsystem are the normalized traces are called marginal tracial states. We investigate extremal marginal tracial states and compute their maximal rank. Diagonal marginal tracial states are also considered.

FACTORS GENERATED BY C*-FINITELY CORRELATED STATES

The possibility of detecting correlations between two quantum-mechanical systems from only the information of a subsystem is investigated. For generic cases, we prove that there exist correlations between two quantum systems if the time derivative of the reduced purity is not zero. Therefore, an experimentalist can conclude that correlations between the system and some environment are nonzero if the time derivative of the reduced purity is found not to be zero. A quantitative estimation of the time derivative of the reduced purity with respect to correlations is also given. This clarifies the role of correlations in the mechanism of decoherence in open quantum systems.

Dynamical Entropy of Generalized Quantum Markov Chains on Gauge-invariant C *-algebras

General property of the relation between the dynamics of reduced purity and correlations in quantum mechanical systems is investigated. We show that a non-zero time-derivative of the reduced purity of a system implies the existence of non-zero correlations with its environment for any unbounded Hamiltonian with finite variance. This shows the impact of local dynamical information on the correlations, as well as the role of correlations in the mechanism of purity change.

Non-commutative hypergroup of order five

We present several equivalent conditions for C*-finitely correlated states defined on the UHF algebras to be factor states and consider the types of factors generated by them. Subfactors generated by generalized quantum Markov chains defined on the gauge-invariant parts of the UHF algebras are also discussed.