Publications and Preprints
Quantum Stochastic Calculus and Quantum Gaussian Processes
by
K. R. Parthasarathy
In this lecture we present a brief outline of boson Fock space
stochastic calculus based on the creation, conservation and
annihilation operators of free field theory, as given in the 1984
paper of Hudson and Parthasarathy. We show how a part of this
architecture yields Gaussian fields stationary under a group
action. Then we introduce the notion of semigroups of quasifree
completely positive maps on the algebra of all bounded operators in
the boson Fock space $\Gamma (\mathbb{C}^n)$ over $\mathbb{C}^n.$
These semigroups are not strongly continuous but their preduals map
Gaussian states to Gaussian states. They were first introduced and
their generators were shown to be of the Lindblad type by
Vanheuverzwijn. They were recently investigated in the context of
quantum information theory by Heinosaari, Holevo and Wolf. Here we
present the exact noisy Schr\"odinger equation which dilates such a
semigroup to a quantum Gaussian Markov process.
isid/ms/2014/10 [fulltext]
Click here to return to Preprints Page