arXiv subjects
Publications and source records attributed to Gen Kimura.
Conventional solutions to the (Mean) King's problem without using entanglement have been investigated by Aravind [P. K. Aravind, ``Best conventional solutions to the King's problem'', Z. Naturforsch. 58a, 682 (2003)]. We report that the upper bound for the success probability claimed there is not valid in general, and give a condition for the claim to be justified.
The Mean King's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d=6 or d=10. In contrast to their result, we show that the King's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.
Bloch-vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We show that the maximum radius in each direction, which is due to the construction of the Bloch-vector space, is determined by the minimum eigenvalue of the corresponding observable (orthogonal generator of SU(N)). From this fact, we reveal the dual property of the structure of the Bloch-vector space; if in some direction the space reachs the large sphere (pure state), then in the opposite direction the space can only get to the small sphere, and vice versa. Another application is a parameterization with simple ranges of density operators. We also provide three classes of quantum-state representation based on actual measurements beyond the Bloch vector and discuss their state-spaces.
We determine the set of the Bloch vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.
We examine the validity of the Kraus representation in the presence of initial correlations and show that it is assured only when a joint dynamics is locally unitary.
We discuss a restriction on relaxation times derived from the Lindblad-type master equations for 2-level systems and show that none of the inverse relaxation times can be greater than the sum of the others. The relation is experimentally proved or disproved and can be considered to be a measure for or against the applicability of the Lindblad-type master equations and therefore of the so-called completely positive condition.
Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants, which is never observed in the weak-coupling regime. We also discuss inequalities among the relaxation constants in our model and show the well-known relation 2Γ_T >= Γ_L, for example, for a wider parameter region than before.
The stochastic limit approximation method for ``rapid'' decay is presented, where the damping rate γis comparable to the system frequency Ω, i.e., γ\sim Ω, whereas the usual stochastic limit approximation is applied only to the weak damping situation γ<< Ω. The key formulas for rapid decay are very similar to those for weak damping, but the dynamics is quite different. From a microscopic Hamiltonian, the spin-boson model, a Bloch equation containing two independent time scales is derived. This is a useful method to extract the minimal dissipative dynamics at high temperature kT >> \hbarΩand the master equations obtained are of the Lindblad form even for the Caldeira-Leggett model. The validity of the method is confirmed by comparing the master equation derived through this method with the exact one.