12,108 research outputs found
Two examples of vanishing and squeezing in Kâ
Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic K-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when it is the infinite dihedral group in both cases with the family of finite subgroups. We prove a vanishing theorem and show how to explicitly squeeze the generators of these groups in Kâ. For the infinite cyclic group, when taking coefficients in a regular ring, we get a squeezing result for every element of Kâ; this follows from the well-known result of Bass, Heller and Swan.ANII - FCE_3_2018_1_14858
Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states
We derive fidelity benchmarks for the quantum storage and teleportation of
squeezed states of continuous variable systems, for input ensembles where the
degree of squeezing is fixed, no information about its orientation in phase
space is given, and the distribution of phase space displacements is a
Gaussian. In the limit where the latter becomes flat, we prove analytically
that the maximal classical achievable fidelity (which is 1/2 without squeezing,
for ) is given by , vanishing when the degree of squeezing
diverges. For mixed states, as well as for general distributions of
displacements, we reduce the determination of the benchmarks to the solution of
a finite-dimensional semidefinite program, which yields accurate, certifiable
bounds thanks to a rigorous analysis of the truncation error. This approach may
be easily adapted to more general ensembles of input states.Comment: 19 pages, 4figure
Continuous variable entanglement sharing in non-inertial frames
We study the distribution of entanglement between modes of a free scalar
field from the perspective of observers in uniform acceleration. We consider a
two-mode squeezed state of the field from an inertial perspective, and
analytically study the degradation of entanglement due to the Unruh effect, in
the cases of either one or both observers undergoing uniform acceleration. We
find that for two observers undergoing finite acceleration, the entanglement
vanishes between the lowest frequency modes. The loss of entanglement is
precisely explained as a redistribution of the inertial entanglement into
multipartite quantum correlations among accessible and unaccessible modes from
a non-inertial perspective. We show that classical correlations are also lost
from the perspective of two accelerated observers but conserved if one of the
observers remains inertial.Comment: 19 pages, 13 EPS figures (most low-res due to oversize); terminology
revise
Broadband teleportation
Quantum teleportation of an unknown broadband electromagnetic field is
investigated. The continuous-variable teleportation protocol by Braunstein and
Kimble [Phys. Rev. Lett. {\bf 80}, 869 (1998)] for teleporting the quantum
state of a single mode of the electromagnetic field is generalized for the case
of a multimode field with finite bandwith. We discuss criteria for
continuous-variable teleportation with various sets of input states and apply
them to the teleportation of broadband fields. We first consider as a set of
input fields (from which an independent state preparer draws the inputs to be
teleported) arbitrary pure Gaussian states with unknown coherent amplitude
(squeezed or coherent states). This set of input states, further restricted to
an alphabet of coherent states, was used in the experiment by Furusawa {\it et
al.} [Science {\bf 282}, 706 (1998)]. It requires unit-gain teleportation for
optimizing the teleportation fidelity. In our broadband scheme, the excess
noise added through unit-gain teleportation due to the finite degree of the
squeezed-state entanglement is just twice the (entanglement) source's squeezing
spectrum for its ``quiet quadrature.'' The teleportation of one half of an
entangled state (two-mode squeezed vacuum state), i.e., ``entanglement
swapping,'' and its verification are optimized under a certain nonunit gain
condition. We will also give a broadband description of this
continuous-variable entanglement swapping based on the single-mode scheme by
van Loock and Braunstein [Phys. Rev. A {\bf 61}, 10302 (2000)]Comment: 27 pages, 7 figures, revised version for publication, Physical Review
A (August 2000); major changes, in parts rewritte
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