2,648 research outputs found
Conditional quantum dynamics with several observers
We consider several observers who monitor different parts of the environment
of a single quantum system and use their data to deduce its state. We derive a
set of conditional stochastic master equations that describe the evolution of
the density matrices each observer ascribes to the system under the Markov
approximation, and show that this problem can be reduced to the case of a
single "super-observer", who has access to all the acquired data. The key
problem - consistency of the sets of data acquired by different observers - is
then reduced to the probability that a given combination of data sets will be
ever detected by the "super-observer". The resulting conditional master
equations are applied to several physical examples: homodyne detection of
phonons in quantum Brownian motion, photo-detection and homodyne detection of
resonance fluorescence from a two-level atom. We introduce {\it relative
purity} to quantify the correlations between the information about the system
gathered by different observers from their measurements of the environment. We
find that observers gain the most information about the state of the system and
they agree the most about it when they measure the environment observables with
eigenstates most closely correlated with the optimally predictable {\it pointer
basis} of the system.Comment: Updated version: new title and contents. 22 pages, 8 figure
Unconditional Pointer States from Conditional Master Equations
When part of the environment responsible for decoherence is used to extract
information about the decohering system, the preferred {\it pointer states}
remain unchanged. This conclusion -- reached for a specific class of models --
is investigated in a general setting of conditional master equations using
suitable generalizations of predictability sieve. We also find indications that
the einselected states are easiest to infer from the measurements carried out
on the environment.Comment: 4 pages, 3 .eps figures; final version to appear in Phys.Rev.Let
Topological Schr\"odinger cats: Non-local quantum superpositions of topological defects
Topological defects (such as monopoles, vortex lines, or domain walls) mark
locations where disparate choices of a broken symmetry vacuum elsewhere in the
system lead to irreconcilable differences. They are energetically costly (the
energy density in their core reaches that of the prior symmetric vacuum) but
topologically stable (the whole manifold would have to be rearranged to get rid
of the defect). We show how, in a paradigmatic model of a quantum phase
transition, a topological defect can be put in a non-local superposition, so
that - in a region large compared to the size of its core - the order parameter
of the system is "undecided" by being in a quantum superposition of conflicting
choices of the broken symmetry. We demonstrate how to exhibit such a
"Schr\"odinger kink" by devising a version of a double-slit experiment suitable
for topological defects. Coherence detectable in such experiments will be
suppressed as a consequence of interaction with the environment. We analyze
environment-induced decoherence and discuss its role in symmetry breaking.Comment: 7 pages, 4 figure
Testing quantum adiabaticity with quench echo
Adiabaticity of quantum evolution is important in many settings. One example
is the adiabatic quantum computation. Nevertheless, up to now, there is no
effective method to test the adiabaticity of the evolution when the
eigenenergies of the driven Hamiltonian are not known. We propose a simple
method to check adiabaticity of a quantum process for an arbitrary quantum
system. We further propose a operational method for finding a uniformly
adiabatic quench scheme based on Kibble-Zurek mechanism for the case when the
initial and the final Hamiltonians are given. This method should help in
implementing adiabatic quantum computation.Comment: This is a new version. Some typos in the New Journal of Physics
version have been correcte
Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again
We show that a simple approximation based on concepts underlying the
Kibble-Zurek theory of second order phase transition dynamics can be used to
treat avoided level crossing problems. The approach discussed in this paper
provides an intuitive insight into quantum dynamics of two level systems, and
may serve as a link between the theory of dynamics of classical and quantum
phase transitions. To illustrate these ideas we analyze dynamics of a
paramagnet-ferromagnet quantum phase transition in the Ising model. We also
present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys.
Rev.
Probabilities from envariance?
Zurek claims to have derived Born's rule noncircularly in the context of an
ontological no-collapse interpretation of quantum states, without any "deus ex
machina imposition of the symptoms of classicality." After a brief review of
Zurek's derivation it is argued that this claim is exaggerated if not wholly
unjustified. In order to demonstrate that Born's rule arises noncircularly from
deterministically evolving quantum states, it is not sufficient to assume that
quantum states are somehow associated with probabilities and then prove that
these probabilities are given by Born's rule. One has to show how irreducible
probabilities can arise in the context of an ontological no-collapse
interpretation of quantum states. It is argued that the reason why all attempts
to do this have so far failed is that quantum states are fundamentally
algorithms for computing correlations between possible measurement outcomes,
rather than evolving ontological states.Comment: To appear in IJQI; 9 pages, LaTe
Quantum decoherence and classical correlations of the harmonic oscillator in the Lindblad theory
In the framework of the Lindblad theory for open quantum systems we determine
the degree of quantum decoherence and classical correlations of a harmonic
oscillator interacting with a thermal bath. The transition from quantum to
classical behaviour of the considered system is analyzed and it is shown that
the classicality takes place during a finite interval of time. We calculate
also the decoherence time and show that it has the same scale as the time after
which statistical fluctuations become comparable with quantum fluctuations.Comment: 24 pages, 8 figure
A simple example of "Quantum Darwinism": Redundant information storage in many-spin environments
As quantum information science approaches the goal of constructing quantum
computers, understanding loss of information through decoherence becomes
increasingly important. The information about a system that can be obtained
from its environment can facilitate quantum control and error correction.
Moreover, observers gain most of their information indirectly, by monitoring
(primarily photon) environments of the "objects of interest." Exactly how this
information is inscribed in the environment is essential for the emergence of
"the classical" from the quantum substrate. In this paper, we examine how
many-qubit (or many-spin) environments can store information about a single
system. The information lost to the environment can be stored redundantly, or
it can be encoded in entangled modes of the environment. We go on to show that
randomly chosen states of the environment almost always encode the information
so that an observer must capture a majority of the environment to deduce the
system's state. Conversely, in the states produced by a typical decoherence
process, information about a particular observable of the system is stored
redundantly. This selective proliferation of "the fittest information" (known
as Quantum Darwinism) plays a key role in choosing the preferred, effectively
classical observables of macroscopic systems. The developing appreciation that
the environment functions not just as a garbage dump, but as a communication
channel, is extending our understanding of the environment's role in the
quantum-classical transition beyond the traditional paradigm of decoherence.Comment: 21 pages, 6 figures, RevTex 4. Submitted to Foundations of Physics
(Asher Peres Festschrift
Quantum Chaotic Environments, The Butterfly Effect, And Decoherence
We investigate the sensitivity of quantum systems that are chaotic in a
classical limit, to small perturbations of their equations of motion. This
sensitivity, originally studied in the context of defining quantum chaos, is
relevant to decoherence in situations when the environment has a chaotic
classical counterpart.Comment: 4 pages, 3 figure
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