252 research outputs found
Quantum data processing and error correction
This paper investigates properties of noisy quantum information channels. We
define a new quantity called {\em coherent information} which measures the
amount of quantum information conveyed in the noisy channel. This quantity can
never be increased by quantum information processing, and it yields a simple
necessary and sufficient condition for the existence of perfect quantum error
correction.Comment: LaTeX, 20 page
On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy
The challenge of equality in the strong subadditivity inequality of entropy
is approached via a general additivity of correlation information in terms of
nonoverlapping clusters of subsystems in multipartite states (density
operators). A family of tripartite states satisfying equality is derived.Comment: 8 pages; Latex2e and Revtex
Fidelity and Concurrence of conjugated states
We prove some new properties of fidelity (transition probability) and
concurrence, the latter defined by straightforward extension of Wootters
notation. Choose a conjugation and consider the dependence of fidelity or of
concurrence on conjugated pairs of density operators. These functions turn out
to be concave or convex roofs. Optimal decompositions are constructed. Some
applications to two- and tripartite systems illustrate the general theorem.Comment: 10 pages, RevTex, Correction: Enlarged, reorganized version. More
explanation
Analysis of a continuous-variable quadripartite cluster state from a single optical parametric oscillator
We examine the feasibility of generating continuous-variable multipartite
entanglement in an intra-cavity quadruply concurrent downconversion scheme that
has been proposed for the generation of cluster states by Menicucci \textit{et
al.} [Physical Review Letters \textbf{101}, 130501 (2008)]. By calculating
optimized versions of the van Loock-Furusawa correlations we demonstrate
genuine quadripartite entanglement and investigate the degree of entanglement
present. Above the oscillation threshold the basic cluster state geometry under
consideration suffers from phase diffusion. We alleviate this problem by
incorporating a small injected signal into our analysis. Finally, we
investigate squeezed joint operators. While the squeezed joint operators
approach zero in the undepleted regime, we find that this is not the case when
we consider the full interaction Hamiltonian and the presence of a cavity. In
fact, we find that the decay of these operators is minimal in a cavity, and
even depletion alone inhibits cluster state formation.Comment: 26 pages, 12 figure
Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect
We present an efficient quantum algorithm to measure the average fidelity
decay of a quantum map under perturbation using a single bit of quantum
information. Our algorithm scales only as the complexity of the map under
investigation, so for those maps admitting an efficient gate decomposition, it
provides an exponential speed up over known classical procedures. Fidelity
decay is important in the study of complex dynamical systems, where it is
conjectured to be a signature of quantum chaos. Our result also illustrates the
role of chaos in the process of decoherence.Comment: 4 pages, 2 eps figure
Teleportation via thermally entangled state of a two-qubit Heisenberg XX chain
We find that quantum teleportation, using the thermally entangled state of
two-qubit Heisenberg XX chain as a resource, with fidelity better than any
classical communication protocol is possible. However, a thermal state with a
greater amount of thermal entanglement does not necessarily yield better
fidelity. It depends on the amount of mixing between the separable state and
maximally entangled state in the spectra of the two-qubit Heisenberg XX model.Comment: 5 pages, 1 tabl
Renormalization Group and Quantum Information
The renormalization group is a tool that allows one to obtain a reduced
description of systems with many degrees of freedom while preserving the
relevant features. In the case of quantum systems, in particular,
one-dimensional systems defined on a chain, an optimal formulation is given by
White's "density matrix renormalization group". This formulation can be shown
to rely on concepts of the developing theory of quantum information.
Furthermore, White's algorithm can be connected with a peculiar type of
quantization, namely, angular quantization. This type of quantization arose in
connection with quantum gravity problems, in particular, the Unruh effect in
the problem of black-hole entropy and Hawking radiation. This connection
highlights the importance of quantum system boundaries, regarding the
concentration of quantum states on them, and helps us to understand the optimal
nature of White's algorithm.Comment: 16 pages, 5 figures, accepted in Journal of Physics
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Two separated observers, by applying local operations to a supply of
not-too-impure entangled states ({\em e.g.} singlets shared through a noisy
channel), can prepare a smaller number of entangled pairs of arbitrarily high
purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully
teleport unknown quantum states from one observer to the other, thereby
achieving faithful transfrom one observer to the other, thereby achieving
faithful transmission of quantum information through a noisy channel. We give
upper and lower bounds on the yield of pure singlets ()
distillable from mixed states , showing if
\bra{\Psi^-}M\ket{\Psi^-}>\half.Comment: 4 pages (revtex) plus 1 figure (postscript). See also
http://vesta.physics.ucla.edu/~smolin/ . Replaced to correct interchanged
and near top of column 2, page
Simple Realization Of The Fredkin Gate Using A Series Of Two-body Operators
The Fredkin three-bit gate is universal for computational logic, and is
reversible. Classically, it is impossible to do universal computation using
reversible two-bit gates only. Here we construct the Fredkin gate using a
combination of six two-body reversible (quantum) operators.Comment: Revtex 3.0, 7 pages, 3 figures appended at the end, please refer to
the comment lines at the beginning of the manuscript for reasons of
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