arXiv subjects

Motoyuki Yoshida

Publications and source records attributed to Motoyuki Yoshida.

3 recordsLinked to original sources

arXiv2010

Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator

A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the context of the biorthogonal system and the rigged Hilbert space, and the contribution of each eigenprojection to expectation values of physical quantities is revealed. We also construct the ladder operators of the Liouvillian, which clarify the structure of the spectral resolution.

quant-ph↗

arXiv2007

Decrease of entanglement by local operations in the Dür-Cirac method

One cannot always obtain information about entanglement by the Dür-Cirac (DC) method. The impracticality is attributed to the decrease of entanglement by local operations in the DC method. We show that, even in 2--qubit systems, there exist states whose entangled property the DC method never evaluates. The class of such states in 2--qubit systems is completely characterized by the value of the fully entangled fraction. Actually, a state whose fully entangled fraction is less than or equal to 1/2 is always transformed into a separable state by local operations in the DC method, even if it has negative partial transposition.

quant-ph↗

arXiv2007

Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift

Recently, Yu, Brown, and Chuang [Phys. Rev. A {\bf 71}, 032341 (2005)] investigated the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance (NMR). Their research gave an insight into the role of the entanglement in a liquid-state NMR quantum computer. Moreover, they attempted to reveal the role of mixed-state entanglement in quantum computing. However, they assumed that the Zeeman energy of each nuclear spin which corresponds to a qubit takes a common value for all; there is no chemical shift. In this paper, we research a model with the chemical shifts and analytically derive the physical parameter region where unitary transformed thermal states are entangled, by the positive partial transposition (PPT) criterion with respect to any bipartition. We examine the effect of the chemical shifts on the boundary between the separability and the nonseparability, and find it is negligible.

quant-ph↗