326 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
Quantum Darwinism requires an extra-theoretical assumption of encoding redundancy
Observers restricted to the observation of pointer states of apparatus cannot
conclusively demonstrate that the pointer of an apparatus A registers the state
of a system of interest S without perturbing S. Observers cannot, therefore,
conclusively demonstrate that the states of a system S are redundantly encoded
by pointer states of multiple independent apparatus without destroying the
redundancy of encoding. The redundancy of encoding required by quantum
Darwinism must, therefore, be assumed from outside the quantum-mechanical
formalism and without the possibility of experimental demonstration.Comment: 5 pages, 1 figure. Comments on foundational assumptions of W. Zurek
(2009) Nat Phys 5 181 (arXiv 0903.5082). v2 significant revision to improve
clarit
Decoherence, Re-coherence, and the Black Hole Information Paradox
We analyze a system consisting of an oscillator coupled to a field. With the
field traced out as an environment, the oscillator loses coherence on a very
short {\it decoherence timescale}; but, on a much longer {\it relaxation
timescale}, predictably evolves into a unique, pure (ground) state. This
example of {\it re-coherence} has interesting implications both for the
interpretation of quantum theory and for the loss of information during black
hole evaporation. We examine these implications by investigating the
intermediate and final states of the quantum field, treated as an open system
coupled to an unobserved oscillator.Comment: 23 pages, 2 figures included, figures 3.1 - 3.3 available at
http://qso.lanl.gov/papers/Papers.htm
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
Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a Model
Chaotic evolutions exhibit exponential sensitivity to initial conditions.
This suggests that even very small perturbations resulting from weak coupling
of a quantum chaotic environment to the position of a system whose state is a
non-local superposition will lead to rapid decoherence. However, it is also
known that quantum counterparts of classically chaotic systems lose exponential
sensitivity to initial conditions, so this expectation of enhanced decoherence
is by no means obvious. We analyze decoherence due to a "toy" quantum
environment that is analytically solvable, yet displays the crucial phenomenon
of exponential sensitivity to perturbations. We show that such an environment,
with a single degree of freedom, can be far more effective at destroying
quantum coherence than a heat bath with infinitely many degrees of freedom.
This also means that the standard "quantum Brownian motion" model for a
decohering environment may not be as universally applicable as it once was
conjectured to be.Comment: RevTeX, 29 pages, 5 EPS figures. Substantially rewritten analysis,
improved figures, additional references, and errors fixed. Final version (to
appear in PRA
Fragility of a class of highly entangled states of many quantum-bits
We consider a Quantum Computer with n quantum-bits (`qubits'), where each
qubit is coupled independently to an environment affecting the state in a
dephasing or depolarizing way. For mixed states we suggest a quantification for
the property of showing {\it quantum} uncertainty on the macroscopic level. We
illustrate in which sense a large parameter can be seen as an indicator for
large entanglement and give hypersurfaces enclosing the set of separable
states. Using methods of the classical theory of maximum likelihood estimation
we prove that this parameter is decreasing with 1/\sqrt{n} for all those states
which have been exposed to the environment.
Furthermore we consider a Quantum Computer with perfect 1-qubit gates and
2-qubit gates with depolarizing error and show that any state which can be
obtained from a separable initial state lies inbetween a family of pairs of
certain hypersurfaces parallel to those enclosing the separable ones.Comment: 9 Pages, RevTe
Entropy and Wigner Functions
The properties of an alternative definition of quantum entropy, based on
Wigner functions, are discussed. Such definition emerges naturally from the
Wigner representation of quantum mechanics, and can easily quantify the amount
of entanglement of a quantum state. It is shown that smoothing of the Wigner
function induces an increase in entropy. This fact is used to derive some
simple rules to construct positive definite probability distributions which are
also admissible Wigner functionsComment: 18 page
Environment-Induced Decoherence and the Transition From Quantum to Classical
We study dynamics of quantum open systems, paying special attention to those
aspects of their evolution which are relevant to the transition from quantum to
classical. We begin with a discussion of the conditional dynamics of simple
systems. The resulting models are straightforward but suffice to illustrate
basic physical ideas behind quantum measurements and decoherence. To discuss
decoherence and environment-induced superselection einselection in a more
general setting, we sketch perturbative as well as exact derivations of several
master equations valid for various systems. Using these equations we study
einselection employing the general strategy of the predictability sieve.
Assumptions that are usually made in the discussion of decoherence are
critically reexamined along with the ``standard lore'' to which they lead.
Restoration of quantum-classical correspondence in systems that are classically
chaotic is discussed. The dynamical second law -it is shown- can be traced to
the same phenomena that allow for the restoration of the correspondence
principle in decohering chaotic systems (where it is otherwise lost on a very
short time-scale). Quantum error correction is discussed as an example of an
anti-decoherence strategy. Implications of decoherence and einselection for the
interpretation of quantum theory are briefly pointed out.Comment: 80 pages, 7 figures included, Lectures given by both authors at the
72nd Les Houches Summer School on "Coherent Matter Waves", July-August 199
What is "system": the information-theoretic arguments
The problem of "what is 'system'?" is in the very foundations of modern
quantum mechanics. Here, we point out the interest in this topic in the
information-theoretic context. E.g., we point out the possibility to manipulate
a pair of mutually non-interacting, non-entangled systems to employ
entanglement of the newly defined '(sub)systems' consisting the one and the
same composite system. Given the different divisions of a composite system into
"subsystems", the Hamiltonian of the system may perform in general
non-equivalent quantum computations. Redefinition of "subsystems" of a
composite system may be regarded as a method for avoiding decoherence in the
quantum hardware. In principle, all the notions refer to a composite system as
simple as the hydrogen atom.Comment: 13 pages, no figure
Decoherence in Bose-Einstein Condensates: towards Bigger and Better Schroedinger Cats
We consider a quantum superposition of Bose-Einstein condensates in two
immiscible internal states. A decoherence rate for the resulting Schroedinger
cat is calculated and shown to be a significant threat to this macroscopic
quantum superposition of BEC's. An experimental scenario is outlined where the
decoherence rate due to the thermal cloud is dramatically reduced thanks to
trap engineering and "symmetrization" of the environment which allow for the
Schroedinger cat to be an approximate pointer states.Comment: 12 pages in RevTex; improved presentation; a new comment on
decoherence-free pointer subspaces in BEC; accepted in Phys.Rev.
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