16,117 research outputs found
Communication Enhancement Through Quantum Coherent Control of Channels in an Indefinite Causal-order Scenario
In quantum Shannon theory, transmission of information is enhanced by quantum
features. Up to very recently, the trajectories of transmission remained fully
classical. Recently, a new paradigm was proposed by playing quantum tricks on
two completely depolarizing quantum channels i.e. using coherent control in
space or time of the two quantum channels. We extend here this control to the
transmission of information through a network of an arbitrary number of
channels with arbitrary individual capacity i.e. information preservation
characteristics in the case of indefinite causal order. We propose a formalism
to assess information transmission in the most general case of channels in
an indefinite causal order scenario yielding the output of such transmission.
Then we explicitly derive the quantum switch output and the associated Holevo
limit of the information transmission for , as a function of all
involved parameters. We find in the case that the transmission of
information for three channels is twice of transmission of the two channel case
when a full superposition of all possible causal orders is used
Factoring Safe Semiprimes with a Single Quantum Query
Shor's factoring algorithm (SFA), by its ability to efficiently factor large
numbers, has the potential to undermine contemporary encryption. At its heart
is a process called order finding, which quantum mechanics lets us perform
efficiently. SFA thus consists of a \emph{quantum order finding algorithm}
(QOFA), bookended by classical routines which, given the order, return the
factors. But, with probability up to , these classical routines fail, and
QOFA must be rerun. We modify these routines using elementary results in number
theory, improving the likelihood that they return the factors.
The resulting quantum factoring algorithm is better than SFA at factoring
safe semiprimes, an important class of numbers used in cryptography. With just
one call to QOFA, our algorithm almost always factors safe semiprimes. As well
as a speed-up, improving efficiency gives our algorithm other, practical
advantages: unlike SFA, it does not need a randomly picked input, making it
simpler to construct in the lab; and in the (unlikely) case of failure, the
same circuit can be rerun, without modification.
We consider generalizing this result to other cases, although we do not find
a simple extension, and conclude that SFA is still the best algorithm for
general numbers (non safe semiprimes, in other words). Even so, we present some
simple number theoretic tricks for improving SFA in this case.Comment: v2 : Typo correction and rewriting for improved clarity v3 : Slight
expansion, for improved clarit
Exact Results in SO(11) SUSY Gauge Theories with Spinor and Vector Matter
We investigate the confining phase vacuum structure of supersymmetric SO(11)
gauge theories with one spinor matter field and Nf \le 6 vectors. We describe
several useful tricks and tools that facilitate the analysis of these chiral
models and many other theories of similar type. The forms of the Nf=5 and Nf=6
quantum moduli spaces are deduced by requiring that they reproduce known
results for SU(5) SUSY QCD along the spinor flat direction. After adding mass
terms for vector fields and integrating out heavy degrees of freedom, we also
determine the dynamically generated superpotentials in the Nf \le 4 quantum
theories. We close with some remarks regarding magnetic duals to the Nf \ge 7
electric SO(11) theories.Comment: 16 pages, harvmac and tables macro
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