42,795 research outputs found
Image transfer through a chaotic channel by intensity correlations
The three-wave mixing processes in a second-order nonlinear medium can be
used for imaging protocols, in which an object field is injected into the
nonlinear medium together with a reference field and an image field is
generated. When the reference field is chaotic, the image field is also chaotic
and does not carry any information about the object. We show that a clear image
of the object be extracted from the chaotic image field by measuring the
spatial intensity correlations between this field and one Fourier component of
the reference. We experimentally verify this imaging protocol in the case of
frequency downconversion.Comment: 17 pages, 7 figure
Merits and Qualms of Work Fluctuations in Classical Fluctuation Theorems
Work is one of the most basic notion in statistical mechanics, with work
fluctuation theorems being one central topic in nanoscale thermodynamics. With
Hamiltonian chaos commonly thought to provide a foundation for classical
statistical mechanics, here we present general salient results regarding how
(classical) Hamiltonian chaos generically impacts on nonequilibrium work
fluctuations. For isolated chaotic systems prepared with a microcanonical
distribution, work fluctuations are minimized and vanish altogether in
adiabatic work protocols. For isolated chaotic systems prepared at an initial
canonical distribution at inverse temperature , work fluctuations
depicted by the variance of are also minimized by adiabatic work
protocols. This general result indicates that if the variance of
diverges for an adiabatic work protocol, then it diverges for all nonadiabatic
work protocols sharing the same initial and final Hamiltonians. How such
divergence explicitly impacts on the efficiency of using the Jarzynski's
equality to simulate free energy differences is studied in a Sinai model. Our
general insights shall boost studies in nanoscale thermodynamics and are of
fundamental importance in designing useful work protocols.Comment: 11 pages, 5 figures, close to published versio
Entanglement, randomness and chaos
Entanglement is not only the most intriguing feature of quantum mechanics,
but also a key resource in quantum information science. The entanglement
content of random pure quantum states is almost maximal; such states find
applications in various quantum information protocols. The preparation of a
random state or, equivalently, the implementation of a random unitary operator,
requires a number of elementary one- and two-qubit gates that is exponential in
the number n_q of qubits, thus becoming rapidly unfeasible when increasing n_q.
On the other hand, pseudo-random states approximating to the desired accuracy
the entanglement properties of true random states may be generated efficiently,
that is, polynomially in n_q. In particular, quantum chaotic maps are efficient
generators of multipartite entanglement among the qubits, close to that
expected for random states. This review discusses several aspects of the
relationship between entanglement, randomness and chaos. In particular, I will
focus on the following items: (i) the robustness of the entanglement generated
by quantum chaotic maps when taking into account the unavoidable noise sources
affecting a quantum computer; (ii) the detection of the entanglement of
high-dimensional (mixtures of) random states, an issue also related to the
question of the emergence of classicality in coarse grained quantum chaotic
dynamics; (iii) the decoherence induced by the coupling of a system to a
chaotic environment, that is, by the entanglement established between the
system and the environment.Comment: Review paper, 40 pages, 7 figures, added reference
Simulating noisy quantum protocols with quantum trajectories
The theory of quantum trajectories is applied to simulate the effects of
quantum noise sources induced by the environment on quantum information
protocols. We study two models that generalize single qubit noise channels like
amplitude damping and phase flip to the many-qubit situation. We calculate the
fidelity of quantum information transmission through a chaotic channel using
the teleportation scheme with different environments. In this example, we
analyze the role played by the kind of collective noise suffered by the quantum
processor during its operation. We also investigate the stability of a quantum
algorithm simulating the quantum dynamics of a paradigmatic model of chaos, the
baker's map. Our results demonstrate that, using the quantum trajectories
approach, we are able to simulate quantum protocols in the presence of noise
and with large system sizes of more than 20 qubits.Comment: 11 pages, 7 fig
Cutting and Shuffling a Line Segment: Mixing by Interval Exchange Transformations
We present a computational study of finite-time mixing of a line segment by
cutting and shuffling. A family of one-dimensional interval exchange
transformations is constructed as a model system in which to study these types
of mixing processes. Illustrative examples of the mixing behaviors, including
pathological cases that violate the assumptions of the known governing theorems
and lead to poor mixing, are shown. Since the mathematical theory applies as
the number of iterations of the map goes to infinity, we introduce practical
measures of mixing (the percent unmixed and the number of intermaterial
interfaces) that can be computed over given (finite) numbers of iterations. We
find that good mixing can be achieved after a finite number of iterations of a
one-dimensional cutting and shuffling map, even though such a map cannot be
considered chaotic in the usual sense and/or it may not fulfill the conditions
of the ergodic theorems for interval exchange transformations. Specifically,
good shuffling can occur with only six or seven intervals of roughly the same
length, as long as the rearrangement order is an irreducible permutation. This
study has implications for a number of mixing processes in which
discontinuities arise either by construction or due to the underlying physics.Comment: 21 pages, 10 figures, ws-ijbc class; accepted for publication in
International Journal of Bifurcation and Chao
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