1,704 research outputs found
Carmichael Numbers on a Quantum Computer
We present a quantum probabilistic algorithm which tests with a polynomial
computational complexity whether a given composite number is of the Carmichael
type. We also suggest a quantum algorithm which could verify a conjecture by
Pomerance, Selfridge and Wagstaff concerning the asymptotic distribution of
Carmichael numbers smaller than a given integer.Comment: 7 pages, Latex/REVTEX fil
Quantum Brachistochrone for Mixed States
We present a general formalism based on the variational principle for finding
the time-optimal quantum evolution of mixed states governed by a master
equation, when the Hamiltonian and the Lindblad operators are subject to
certain constraints. The problem reduces to solving first a fundamental
equation (the {\it quantum brachistochrone}) for the Hamiltonian, which can be
written down once the constraints are specified, and then solving the
constraints and the master equation for the Lindblad and the density operators.
As an application of our formalism, we study a simple one-qubit model where the
optimal Lindblad operators control decoherence and can be simulated by a
tunable coupling with an ancillary qubit. It is found that the evolution
through mixed states can be more efficient than the unitary evolution between
given pure states. We also discuss the mixed state evolution as a finite time
unitary evolution of the system plus an environment followed by a single
measurement. For the simplest choice of the constraints, the optimal duration
time for the evolution is an exponentially decreasing function of the
environment's degrees of freedom.Comment: 8 pages, 3 figure
Comments on Closed Bianchi Models
We show several kinematical properties that are intrinsic to the Bianchi
models with compact spatial sections. Especially, with spacelike hypersurfaces
being closed, (A) no anisotropic expansion is allowed for Bianchi type V and
VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to
show them, we put into geometric terms what is meant by spatial homogeneity and
employ a mathematical result on 3-manifolds. We make clear the relation between
the Bianchi type symmetry of space-time and spatial compactness, some part of
which seem to be unnoticed in the literature. Especially, it is shown under
what conditions class B Bianchi models do not possess compact spatial sections.
Finally we briefly describe how this study is useful in investigating global
dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5
Complementarity of Entanglement and Interference
A complementarity relation is shown between the visibility of interference
and bipartite entanglement in a two qubit interferometric system when the
parameters of the quantum operation change for a given input state. The
entanglement measure is a decreasing function of the visibility of
interference. The implications for quantum computation are briefly discussed.Comment: Final version, to appear on IJMPC; minor revision
Quantum Entropy Bound by Information in Black Hole Spacetime
We show that the increase of the generalized entropy by a quantum process outside the horizon of a black hole is more than the Holevo bound of the classical information lost into the black hole and which could be obtained by further observations outside the horizon. In the optimal case, the prepared information can be completely retrieved
Relative information entropy of an inhomogeneous universe
In the context of averaging an inhomogeneous cosmological model, we propose a
natural measure identical to the Kullback-Leibler relative information entropy,
which expresses the distinguishability of the local inhomogeneous density field
from its spatial average on arbitrary compact domains. This measure is expected
to be an increasing function in time and thus to play a significant role in
studying gravitational entropy. To verify this conjecture, we explore the time
evolution of the measure using the linear perturbation theory of a spatially
flat FLRW model and a spherically symmetric nonlinear solution. We discuss the
generality and conditions for the time-increasing nature of the measure, and
also the connection to the backreaction effect caused by inhomogeneities.Comment: 9 pages, 4 figures, LaTeX 2e using aipproc.cls, published in AIP
Conf. Proc., minor corrections mad
Quantum Computers and Classical Randomized Algorithms
We present a quantum version of the classical probabilistic algorithms Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main novelties of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes
A Modular Invariant Quantum Theory From the Connection Formulation of (2+1)-Gravity on the Torus
By choosing an unconventional polarization of the connection phase space in
(2+1)-gravity on the torus, a modular invariant quantum theory is constructed.
Unitary equivalence to the ADM-quantization is shown.Comment: Latex, 4 page
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