395 research outputs found
Quantum Weakly Nondeterministic Communication Complexity
We study the weakest model of quantum nondeterminism in which a classical
proof has to be checked with probability one by a quantum protocol. We show the
first separation between classical nondeterministic communication complexity
and this model of quantum nondeterministic communication complexity for a total
function. This separation is quadratic.Comment: 12 pages. v3: minor correction
A faster pseudo-primality test
We propose a pseudo-primality test using cyclic extensions of . For every positive integer , this test achieves the
security of Miller-Rabin tests at the cost of Miller-Rabin
tests.Comment: Published in Rendiconti del Circolo Matematico di Palermo Journal,
Springe
A BQP-complete problem related to the Ising model partition function via a new connection between quantum circuits and graphs
We present a simple construction that maps quantum circuits to graphs and
vice-versa. Inspired by the results of D.A. Lidar linking the Ising partition
function with quadratically signed weight enumerators (QWGTs), we also present
a BQP-complete problem for the additive approximation of a function over
hypergraphs related to the generating function of Eulerian subgraphs for
ordinary graphs. We discuss connections with the Ising partition function.Comment: 12 pages, 2 figure
Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
In classical information theory, entropy rate and Kolmogorov complexity per
symbol are related by a theorem of Brudno. In this paper, we prove a quantum
version of this theorem, connecting the von Neumann entropy rate and two
notions of quantum Kolmogorov complexity, both based on the shortest qubit
descriptions of qubit strings that, run by a universal quantum Turing machine,
reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in
the Communications in Mathematical Physics
(http://www.springerlink.com/content/1432-0916/
Tunneling of quantum rotobreathers
We analyze the quantum properties of a system consisting of two nonlinearly
coupled pendula. This non-integrable system exhibits two different symmetries:
a permutational symmetry (permutation of the pendula) and another one related
to the reversal of the total momentum of the system. Each of these symmetries
is responsible for the existence of two kinds of quasi-degenerated states. At
sufficiently high energy, pairs of symmetry-related states glue together to
form quadruplets. We show that, starting from the anti-continuous limit,
particular quadruplets allow us to construct quantum states whose properties
are very similar to those of classical rotobreathers. By diagonalizing
numerically the quantum Hamiltonian, we investigate their properties and show
that such states are able to store the main part of the total energy on one of
the pendula. Contrary to the classical situation, the coupling between pendula
necessarily introduces a periodic exchange of energy between them with a
frequency which is proportional to the energy splitting between
quasi-degenerated states related to the permutation symmetry. This splitting
may remain very small as the coupling strength increases and is a decreasing
function of the pair energy. The energy may be therefore stored in one pendulum
during a time period very long as compared to the inverse of the internal
rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl
Effective Lagrangian Approach to the Theory of Eta Photoproduction in the Region
We investigate eta photoproduction in the resonance region
within the effective Lagrangian approach (ELA), wherein leading contributions
to the amplitude at the tree level are taken into account. These include the
nucleon Born terms and the leading -channel vector meson exchanges as the
non-resonant pieces. In addition, we consider five resonance contributions in
the - and - channel; besides the dominant , these are:
and . The amplitudes for the
and the photoproduction near threshold have significant
differences, even as they share common contributions, such as those of the
nucleon Born terms. Among these differences, the contribution to the
photoproduction of the -channel excitation of the is the most
significant. We find the off-shell properties of the spin-3/2 resonances to be
important in determining the background contributions. Fitting our effective
amplitude to the available data base allows us to extract the quantity
, characteristic of the
photoexcitation of the resonance and its decay into the
-nucleon channel, of interest to precise tests of hadron models. At the
photon point, we determine it to be from
the old data base, and from a
combination of old data base and new Bates data. We obtain the helicity
amplitude for to be from the old data base, and from the combination of the old data base and new Bates
data, compared with the results of the analysis of pion photoproduction
yielding , in the same units.Comment: 43 pages, RevTeX, 9 figures available upon request, to appear in
Phys. Rev.
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