886 research outputs found
On Markovian Cocycle Perturbations in Classical and Quantum Probability
We introduce Markovian cocycle perturbations of the groups of transformations
associated with the classical and quantum stochastic processes with stationary
increments, which are characterized by a localization of the perturbation to
the algebra of events of the past. It is namely the definition one needs
because the Markovian perturbations of the Kolmogorov flows associated with the
classical and quantum noises result in the perturbed group of transformations
which can be decomposed in the sum of a part associated with deterministic
stochastic processes lying in the past and a part associated with the noise
isomorphic to the initial one. This decomposition allows to obtain some analog
of the Wold decomposition for classical stationary processes excluding a
nondeterministic part of the process in the case of the stationary quantum
stochastic processes on the von Neumann factors which are the Markovian
perturbations of the quantum noises. For the classical stochastic process with
noncorrelated increaments it is constructed the model of Markovian
perturbations describing all Markovian cocycles up to a unitary equivalence of
the perturbations. Using this model we construct Markovian cocyclies
transformating the Gaussian state to the Gaussian states equivalent to
.Comment: 27 page
On tomographic representation on the plane of the space of Schwartz operators and its dual
It is shown that the set of optical quantum tomograms can be provided with
the topology of Frechet space. In such a case the conjugate space will consist
of symbols of quantum observables including all polynomials of the position and
momentum operators.Comment: 9 page
New multiplicativity results for qubit maps
Let be a trace-preserving, positivity-preserving (but not necessarily
completely positive) linear map on the algebra of complex
matrices, and let be any finite-dimensional completely positive map.
For and , we prove that the maximal -norm of the product map
\Phi \ot \Omega is the product of the maximal -norms of and
. Restricting to the class of completely positive maps, this
settles the multiplicativity question for all qubit channels in the range of
values .Comment: 14 pages; original proof simplified by using Gorini and Sudarshan's
classification of extreme affine maps on R^
Entanglement-enhanced classical capacity of two-qubit quantum channels with memory: the exact solution
The maximal amount of information which is reliably transmitted over two uses
of general Pauli channels with memory is proven to be achieved by maximally
entangled states beyond some memory threshold. In particular, this proves a
conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A
{\bf 65}, 050301(R) (2002)]. Below the memory threshold, for arbitrary Pauli
channels, the two-use classical capacity is only achieved by a particular type
of product states.Comment: 5 page
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