3,162 research outputs found
Quantum Stochastic Calculus and Quantum Gaussian Processes
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
over 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
On the maximal dimension of a completely entangled subspace for finite level quantum systems
Let be a finite dimensional complex Hilbert space of
dimension associated with a finite level quantum system for . A subspace is said to be {\it completely entangled} if it has no nonzero
product vector of the form with
in for each . Using the methods of elementary linear algebra
and the intersection theorem for projective varieties in basic algebraic
geometry we prove that where is the collection of all
completely entangled subspaces.
When and an explicit orthonormal
basis of a maximal completely entangled subspace of is given.
We also introduce a more delicate notion of a {\it perfectly entangled}
subspace for a multipartite quantum system, construct an example using the
theory of stabilizer quantum codes and pose a problem
- β¦