5,288 research outputs found
Geometric phases under the presence of a composite environment
We compute the geometric phase for a spin-1/2 particle under the presence of
a composite environment, composed of an external bath (modeled by an infinite
set of harmonic oscillators) and another spin-1/2 particle. We consider both
cases: an initial entanglement between the spin-1/2 particles and an initial
product state in order to see if the initial entanglement has an enhancement
effect on the geometric phase of one of the spins. We follow the nonunitary
evolution of the reduced density matrix and evaluate the geometric phase for a
single two-level system. We also show that the initial entanglement enhances
the sturdiness of the geometric phase under the presence of an external
composite environment.Comment: 10 pages, 12 figures. Version to appear in Phys. Rev.
Predictability sieve, pointer states, and the classicality of quantum trajectories
We study various measures of classicality of the states of open quantum
systems subject to decoherence. Classical states are expected to be stable in
spite of decoherence, and are thought to leave conspicuous imprints on the
environment. Here these expected features of environment-induced superselection
(einselection) are quantified using four different criteria: predictability
sieve (which selects states that produce least entropy), purification time
(which looks for states that are the easiest to find out from the imprint they
leave on the environment), efficiency threshold (which finds states that can be
deduced from measurements on a smallest fraction of the environment), and
purity loss time (that looks for states for which it takes the longest to lose
a set fraction of their initial purity). We show that when pointer states --
the most predictable states of an open quantum system selected by the
predictability sieve -- are well defined, all four criteria agree that they are
indeed the most classical states. We illustrate this with two examples: an
underdamped harmonic oscillator, for which coherent states are unanimously
chosen by all criteria, and a free particle undergoing quantum Brownian motion,
for which most criteria select almost identical Gaussian states (although, in
this case, predictability sieve does not select well defined pointer states.)Comment: 10 pages, 13 figure
Factoring in a Dissipative Quantum Computer
We describe an array of quantum gates implementing Shor's algorithm for prime
factorization in a quantum computer. The array includes a circuit for modular
exponentiation with several subcomponents (such as controlled multipliers,
adders, etc) which are described in terms of elementary Toffoli gates. We
present a simple analysis of the impact of losses and decoherence on the
performance of this quantum factoring circuit. For that purpose, we simulate a
quantum computer which is running the program to factor N = 15 while
interacting with a dissipative environment. As a consequence of this
interaction randomly selected qubits may spontaneously decay. Using the results
of our numerical simulations we analyze the efficiency of some simple error
correction techniques.Comment: plain tex, 18 pages, 8 postscript figure
Dynamics of Open Bosonic Quantum Systems in Coherent State Representation
We consider the problem of decoherence and relaxation of open bosonic quantum
systems from a perspective alternative to the standard master equation or
quantum trajectories approaches. Our method is based on the dynamics of
expectation values of observables evaluated in a coherent state representation.
We examine a model of a quantum nonlinear oscillator with a density-density
interaction with a collection of environmental oscillators at finite
temperature. We derive the exact solution for dynamics of observables and
demonstrate a consistent perturbation approach.Comment: 7 page
Lorentz invariant intrinsic decoherence
Quantum decoherence can arise due to classical fluctuations in the parameters
which define the dynamics of the system. In this case decoherence, and
complementary noise, is manifest when data from repeated measurement trials are
combined. Recently a number of authors have suggested that fluctuations in the
space-time metric arising from quantum gravity effects would correspond to a
source of intrinsic noise, which would necessarily be accompanied by intrinsic
decoherence. This work extends a previous heuristic modification of
Schr\"{o}dinger dynamics based on discrete time intervals with an intrinsic
uncertainty. The extension uses unital semigroup representations of space and
time translations rather than the more usual unitary representation, and does
the least violence to physically important invariance principles. Physical
consequences include a modification of the uncertainty principle and a
modification of field dispersion relations, in a way consistent with other
modifications suggested by quantum gravity and string theory .Comment: This paper generalises an earlier model published as Phys. Rev. A
vol44, 5401 (1991
Decoherence, tunneling and noise-activation in a double-potential well at high and zero temperature
We study the effects of the environment on tunneling in an open system
described by a static double-well potential. We describe the evolution of a
quantum state localized in one of the minima of the potential at , both in
the limits of high and zero environment temperature. We show that the evolution
of the system can be summarized in terms of three main physical phenomena,
namely decoherence, quantum tunneling and noise-induced activation, and we
obtain analytical estimates for the corresponding time-scales. These analytical
predictions are confirmed by large-scale numerical simulations, providing a
detailed picture of the main stages of the evolution and of the relevant
dynamical processes.Comment: Version to appear in Phys. Rev. E. 15 pages, 12 figures (low quality
due to upload size limitations). Good quality figures in a pdf file can be
downloaded from http://www.df.uba.ar/users/lombardo/tunne
Quantum computation with phase drift errors
We present results of numerical simulations of the evolution of an ion trap
quantum computer made out of 18 ions which are subject to a sequence of nearly
15000 laser pulses in order to find the prime factors of N=15. We analyze the
effect of random and systematic phase drift errors arising from inaccuracies in
the laser pulses which induce over (under) rotation of the quantum state.
Simple analytic estimates of the tolerance for the quality of driving pulses
are presented. We examine the use of watchdog stabilization to partially
correct phase drift errors concluding that, in the regime investigated, it is
rather inefficient.Comment: 5 pages, RevTex, 2 figure
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