1,088 research outputs found

### Reversibility conditions for quantum channels and their applications

A necessary condition for reversibility (sufficiency) of a quantum channel
with respect to complete families of states with bounded rank is obtained. A
full description (up to isometrical equivalence) of all quantum channels
reversible with respect to orthogonal and nonorthogonal complete families of
pure states is given. Some applications in quantum information theory are
considered.
The main results can be formulated in terms of the operator algebras theory
(as conditions for reversibility of channels between algebras of all bounded
operators).Comment: 28 pages, this version contains strengthened results of the previous
one and of arXiv:1106.3297; to appear in Sbornik: Mathematics, 204:7 (2013

### Transition probabilities between quasifree states

We obtain a general formula for the transition probabilities between any
state of the algebra of the canonical commutation relations (CCR-algebra) and a
squeezed quasifree state. Applications of this formula are made for the case of
multimode thermal squeezed states of quantum optics using a general canonical
decomposition of the correlation matrix valid for any quasifree state. In the
particular case of a one mode CCR-algebra we show that the transition
probability between two quasifree squeezed states is a decreasing function of
the geodesic distance between the points of the upper half plane representing
these states. In the special case of the purification map it is shown that the
transition probability between the state of the enlarged system and the product
state of real and fictitious subsystems can be a measure for the entanglement.Comment: 13 pages, REVTeX, no figure

### Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results

A formulation of the generalized minimal output entropy conjecture for
Gaussian channels is presented. It asserts that, for states with fixed input
entropy, the minimal value of the output entropy of the channel (i.e. the
minimal output entropy increment for fixed input entropy) is achieved by
Gaussian states. In the case of centered channels (i.e. channels which do not
add squeezing to the input state) this implies that the minimum is obtained by
thermal (Gibbs) inputs. The conjecture is proved to be valid in some special
cases.Comment: 7 pages, updated version minor typos correcte

### On entanglement-assisted classical capacity

This paper is essentially a lecture from the author's course on quantum
information theory, which is devoted to the result of C. H. Bennett, P. W.
Shor, J. A. Smolin and A. V. Thapliyal (quant-ph/0106052) concerning
entanglement-assisted classical capacity of a quantum channel. A modified proof
of this result is given and relation between entanglement-assisted and
unassisted classical capacities is discussed.Comment: 10 pages, LATE

### The optimal unitary dilation for bosonic Gaussian channels

A generic quantum channel can be represented in terms of a unitary
interaction between the information-carrying system and a noisy environment.
Here, the minimal number of quantum Gaussian environmental modes required to
provide a unitary dilation of a multi-mode bosonic Gaussian channel is analyzed
both for mixed and pure environment corresponding to the Stinespring
representation. In particular, for the case of pure environment we compute this
quantity and present an explicit unitary dilation for arbitrary bosonic
Gaussian channel. These results considerably simplify the characterization of
these continuous-variable maps and can be applied to address some open issues
concerning the transmission of information encoded in bosonic systems.Comment: 9 page

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