Master-Equation Formulations of Decoherence

B. Vacchini

Bernard Gaveau, Guy Rideau

Michael J. W. Hall

It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is block-diagonal, then the necessary and sufficient conditions for completely positive evolution may be formulated in terms of the oscillator Hamiltonian or Lagrangian. When the solution of the oscillator equation is not known, an explicit sufficient condition for complete positivity can still be obtained, based on a Hamiltonian/Lagrangian inequality. A rotational form-invariance property is used to characterize the evolution via a single first-order nonlinear differential equation, enabling some further exact results to be obtained. A class of master equations is identified for which complete positivity reduces to the simpler condition of positivity.

Tetsuya Yoneda, Aya Nagasato, Tatsuo Akamine +1 more

Mio Murao

A quantum statistical model for the relaxation of two strongly coupled spin 1/2 particles toward thermal equilibrium is formulated microscopically using a master equation. Raman-type dissipation mechanisms are introduced in addition to the usual bilinear coupling between the coupled system and the reservoir. The effects of two different rotating wave approximations to derive the master equation are investigated. Decoherence is considered as a process toward thermal equilibrium for the dissipative system and is studied by observing the phase and energy relaxation.

Round Table, Hervé Zwirn C