154 research outputs found
Quantum Walks of SU(2)_k Anyons on a Ladder
We study the effects of braiding interactions on single anyon dynamics using
a quantum walk model on a quasi-1-dimensional ladder filled with stationary
anyons. The model includes loss of information of the coin and nonlocal fusion
degrees of freedom on every second time step, such that the entanglement
between the position states and the exponentially growing auxiliary degrees of
freedom is lost. The computational complexity of numerical calculations reduces
drastically from the fully coherent anyonic quantum walk model, allowing for
relatively long simulations for anyons which are spin-1/2 irreps of SU(2)_k
Chern-Simons theory. We find that for Abelian anyons, the walk retains the
ballistic spreading velocity just like particles with trivial braiding
statistics. For non-Abelian anyons, the numerical results indicate that the
spreading velocity is linearly dependent on the number of time steps. By
approximating the Kraus generators of the time evolution map by circulant
matrices, it is shown that the spatial probability distribution for the k=2
walk, corresponding to Ising model anyons, is equal to the classical unbiased
random walk distribution.Comment: 12 pages, 4 figure
Non-positivity of the Wigner function and bounds on associated integrals
The Wigner function shares several properties with classical distribution
functions on phase space, but is not positive-definite. The integral of the
Wigner function over a given region of phase space can therefore lie outside
the interval [0,1]. The problem of finding best-possible upper and lower bounds
for a given region is the problem of finding the greatest and least eigenvalues
of an associated Hermitian operator. Exactly solvable examples are described,
and possible extensions are indicated.Comment: 5 pages, Latex2e fil
Prime decomposition and correlation measure of finite quantum systems
Under the name prime decomposition (pd), a unique decomposition of an
arbitrary -dimensional density matrix into a sum of seperable density
matrices with dimensions given by the coprime factors of is introduced. For
a class of density matrices a complete tensor product factorization is
achieved. The construction is based on the Chinese Remainder Theorem and the
projective unitary representation of by the discrete Heisenberg group
. The pd isomorphism is unitarily implemented and it is shown to be
coassociative and to act on as comultiplication. Density matrices with
complete pd are interpreted as grouplike elements of . To quantify the
distance of from its pd a trace-norm correlation index is
introduced and its invariance groups are determined.Comment: 9 pages LaTeX. Revised version: changes in the terminology, updates
in ref
Quantization of Soliton Cellular Automata
A method of quantization of classical soliton cellular automata (QSCA) is put
forward that provides a description of their time evolution operator by means
of quantum circuits that involve quantum gates from which the associated
Hamiltonian describing a quantum chain model is constructed.
The intrinsic parallelism of QSCA, a phenomenon first known from quantum
computers, is also emphasized.Comment: Latex, 6 pages, 1 figure in eps format included. Submitted to Journal
of Nonlinear Mathematical Physics. Special Issue of Proccedings of NEEDS'9
Complex analytic realizations for quantum algebras
A method for obtaining complex analytic realizations for a class of deformed
algebras based on their respective deformation mappings and their ordinary
coherent states is introduced. Explicit results of such realizations are
provided for the cases of the -oscillators (-Weyl-Heisenberg algebra) and
for the and algebras and their co-products. They are
given in terms of a series in powers of ordinary derivative operators which act
on the Bargmann-Hilbert space of functions endowed with the usual integration
measure. In the limit these realizations reduce to the usual
analytic Bargmann realizations for the three algebras.Comment: 18 page
Free Dirac evolution as a quantum random walk
Any positive-energy state of a free Dirac particle that is initially
highly-localized, evolves in time by spreading at speeds close to the speed of
light. This general phenomenon is explained by the fact that the Dirac
evolution can be approximated arbitrarily closely by a quantum random walk,
where the roles of coin and walker systems are naturally attributed to the spin
and position degrees of freedom of the particle. Initially entangled and
spatially localized spin-position states evolve with asymptotic two-horned
distributions of the position probability, familiar from earlier studies of
quantum walks. For the Dirac particle, the two horns travel apart at close to
the speed of light.Comment: 16 pages, 1 figure. Latex2e fil
Simulation of static and random errors on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer with few qubits
We consider Grover's search algorithm on a model quantum computer implemented
on a chain of four or five nuclear spins with first and second neighbour Ising
interactions. Noise is introduced into the system in terms of random
fluctuations of the external fields. By averaging over many repetitions of the
algorithm, the output state becomes effectively a mixed state. We study its
overlap with the nominal output state of the algorithm, which is called
fidelity. We find either an exponential or a Gaussian decay for the fidelity as
a function of the strength of the noise, depending on the type of noise (static
or random) and whether error supression is applied (the 2pi k-method) or not.Comment: 18 pages, 8 figures, extensive revision with new figure
Geometric phase in open systems
We calculate the geometric phase associated to the evolution of a system
subjected to decoherence through a quantum-jump approach. The method is general
and can be applied to many different physical systems. As examples, two main
source of decoherence are considered: dephasing and spontaneous decay. We show
that the geometric phase is completely insensitive to the former, i.e. it is
independent of the number of jumps determined by the dephasing operator.Comment: 4 pages, 2 figures, RevTe
Decoherence of geometric phase gates
We consider the effects of certain forms of decoherence applied to both
adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit
we illustrate path-dependent sensitivity to anisotropic noise and for two
qubits we quantify the loss of entanglement as a function of decoherence.Comment: 4 pages, 3 figure
Phase-space-region operators and the Wigner function: Geometric constructions and tomography
Quasiprobability measures on a canonical phase space give rise through the action of Weyl's quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations
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