73 research outputs found
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
Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions
Quantum-classical correspondence in conservative chaotic Hamiltonian systems
is examined using a uniform structure measure for quantal and classical phase
space distribution functions. The similarities and differences between quantum
and classical time-evolving distribution functions are exposed by both
analytical and numerical means. The quantum-classical correspondence of
low-order statistical moments is also studied. The results shed considerable
light on quantum-classical correspondence.Comment: 16 pages, 5 figures, to appear in Physical Review
Intrinsic decoherence and classical-quantum correspondence in two coupled delta-kicked rotors
We show that classical-quantum correspondence of center of mass motion in two
coupled delta-kicked rotors can be obtained from intrinsic decoherence of the
system itself which occurs due to the entanglement of the center of mass motion
to the internal degree of freedom without coupling to external environment
General impossible operations in quantum information
We prove a general limitation in quantum information that unifies the
impossibility principles such as no-cloning and no-anticloning. Further, we
show that for an unknown qubit one cannot design a universal Hadamard gate for
creating equal superposition of the original and its complement state.
Surprisingly, we find that Hadamard transformations exist for an unknown qubit
chosen either from the polar or equatorial great circles. Also, we show that
for an unknown qubit one cannot design a universal unitary gate for creating
unequal superpositions of the original and its complement state. We discuss why
it is impossible to design a controlled-NOT gate for two unknown qubits and
discuss the implications of these limitations.Comment: 15 pages, no figures, Discussion about personal quantum computer
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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
Environment-induced dynamical chaos
We examine the interplay of nonlinearity of a dynamical system and thermal
fluctuation of its environment in the ``physical limit'' of small damping and
slow diffusion in a semiclassical context and show that the trajectories of
c-number variables exhibit dynamical chaos due to the thermal fluctuations of
the bath.Comment: Revtex, 4 pages and 4 figure
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Damage evolution and clustering in shock loaded tantalum
Two grades of tantalum were shock loaded by plate impact and recovered. The loading conditions were varied to study the damage evolution in te materials from incipient to full spallation. The authors performed quantitative image analysis and optical profilometry on the recovered specimens. Statistical analyses are shown of the void sizes, void clustering, and void linking in the two material grades
Qubit Disentanglement and Decoherence via Dephasing
We consider whether quantum coherence in the form of mutual entanglement
between a pair of qubits is susceptible to decay that may be more rapid than
the decay of the coherence of either qubit individually. An instance of
potential importance for solid state quantum computing arises if embedded
qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and
local noise at the same time. Here we allow separate phase-noisy channels to
affect local and non-local measures of system coherence. We find that the time
for decay of the qubit entanglement can be significantly shorter than the time
for local dephasing of the individual qubits.Comment: REVTeX, 9 pages, 1 figure, v2 with minor changes, reference adde
Trajectory versus probability density entropy
We study the problem of entropy increase of the Bernoulli-shift map without
recourse to the concept of trajectory and we discuss whether, and under which
conditions if it does, the distribution density entropy coincides with the
Kolmogorov-Sinai entropy, namely, with the trajectory entropy.Comment: 24 page
Fluctuation-dissipation relationship in chaotic dynamics
We consider a general N-degree-of-freedom dissipative system which admits of
chaotic behaviour. Based on a Fokker-Planck description associated with the
dynamics we establish that the drift and the diffusion coefficients can be
related through a set of stochastic parameters which characterize the steady
state of the dynamical system in a way similar to fluctuation-dissipation
relation in non-equilibrium statistical mechanics. The proposed relationship is
verified by numerical experiments on a driven double well system.Comment: Revtex, 23 pages, 2 figure
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