Quantum Stochastic Processes: Boson and Fermion Brownian Motion

Abstract

Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.

A stabilizer code for uncorrelated errors can correct spatially correlated ones

“…In this paper, we prove that errors caused by spatially correlated noise can be corrected by the stabilizer code and error correction operation prepared for uncorrelated ones, and thus, the neglection of spatial correlation is justified. Here, we characterize the noise by quantum Brownian motion [16][17][18][19][20][21] which represents zero-point fluctuation in addition to thermal fluctuation. The time-evolution of both qubits and noise systems is described by the stochastic Liouville equation [16,17,22] within non-equilibrium thermo field dynamics (NETFD) [23][24][25] which is canonical operator formalism for open systems providing us with transparent and powerful methods to tackle problems in quantum information theory, especially, those related to decoherence and/or dissipation.…”

Non-Equilibrium Thermo Field Dynamics and Its Application to Error-Correction for Spatially Correlated Quantum Errors

“…:2 In this section, we confine ourselves to the cases of boson system and of spin system. The extension to the case of fermion system is rather straightforward[33][34][35].Non-Equilibrium Thermo Field Dynamics and Its Application to Error-Correction…”