11,160 research outputs found
Quantum error correction may delay, but also cause, entanglement sudden death
Dissipation may cause two initially entangled qubits to evolve into a
separable state in a finite time. This behavior is called entanglement sudden
death (ESD). We study to what extent quantum error correction can combat ESD.
We find that in some cases quantum error correction can delay entanglement
sudden death but in other cases quantum error correction may cause ESD for
states that otherwise do not suffer from it. Our analysis also shows that
fidelity may not be the best measure to compare the efficiency of different
error correction codes since the fidelity is not directly coupled to a state's
remaining entanglement.Comment: 3 figure
Towards Quantifying Complexity with Quantum Mechanics
While we have intuitive notions of structure and complexity, the
formalization of this intuition is non-trivial. The statistical complexity is a
popular candidate. It is based on the idea that the complexity of a process can
be quantified by the complexity of its simplest mathematical model - the model
that requires the least past information for optimal future prediction. Here we
review how such models, known as -machines can be further simplified
through quantum logic, and explore the resulting consequences for understanding
complexity. In particular, we propose a new measure of complexity based on
quantum -machines. We apply this to a simple system undergoing
constant thermalization. The resulting quantum measure of complexity aligns
more closely with our intuition of how complexity should behave.Comment: 10 pages, 6 figure, Published in the Focus Point on Quantum
information and complexity edition of EPJ Plu
From the superfluid to the Mott regime and back: triggering a non-trivial dynamics in an array of coupled condensates
We consider a system formed by an array of Bose-Einstein condensates trapped
in a harmonic potential with a superimposed periodic optical potential.
Starting from the boson field Hamiltonian, appropriate to describe dilute gas
of bosonic atoms, we reformulate the system dynamics within the Bose-Hubbard
model picture. Then we analyse the effective dynamics of the system when the
optical potential depth is suddenly varied according to a procedure applied in
many of the recent experiments on superfluid-Mott transition in Bose-Einstein
condensates.
Initially the condensates' array generated in a weak optical potential is
assumed to be in the superfluid ground-state which is well described in terms
of coherent states. At a given time, the optical potential depth is suddenly
increased and, after a waiting time, it is quickly decreased so that the
initial depth is restored. We compute the system-state evolution and show that
the potential jump brings on an excitation of the system, incorporated in the
final condensate wave functions, whose effects are analysed in terms of
two-site correlation functions and of on-site population oscillations. Also we
show how a too long waiting time can destroy completely the coherence of the
final state making it unobservable.Comment: 10 pages, 4 figures, to appear on Journal of Physics B (Special
Issue: Levico BEC workshop). Publication status update
Limit cycles of effective theories
A simple example is used to show that renormalization group limit cycles of
effective quantum theories can be studied in a new way. The method is based on
the similarity renormalization group procedure for Hamiltonians. The example
contains a logarithmic ultraviolet divergence that is generated by both real
and imaginary parts of the Hamiltonian matrix elements. Discussion of the
example includes a connection between asymptotic freedom with one scale of
bound states and the limit cycle with an entire hierarchy of bound states.Comment: 8 pages, 3 figures, revtex
What do phase space methods tell us about disordered quantum systems?
Introduction
Phase space methods in quantum mechanics
- The Wigner function
- The Husimi function
- Inverse participation ratio
Anderson model in phase space
- Husimi functions
- Inverse participation ratiosComment: 14 pages, 4 figures. To be published in "The Anderson Transition and
its Ramifications - Localisation, Quantum Interference, and Interactions",
ed. by T. Brandes and S. Kettemann, Lecture Notes in Physics
(http://link.springer.de/series/lnpp/) (Springer Verlag,
Berlin-Heidelberg-New York
More is the Same; Phase Transitions and Mean Field Theories
This paper looks at the early theory of phase transitions. It considers a
group of related concepts derived from condensed matter and statistical
physics. The key technical ideas here go under the names of "singularity",
"order parameter", "mean field theory", and "variational method".
In a less technical vein, the question here is how can matter, ordinary
matter, support a diversity of forms. We see this diversity each time we
observe ice in contact with liquid water or see water vapor, "steam", come up
from a pot of heated water. Different phases can be qualitatively different in
that walking on ice is well within human capacity, but walking on liquid water
is proverbially forbidden to ordinary humans. These differences have been
apparent to humankind for millennia, but only brought within the domain of
scientific understanding since the 1880s.
A phase transition is a change from one behavior to another. A first order
phase transition involves a discontinuous jump in a some statistical variable
of the system. The discontinuous property is called the order parameter. Each
phase transitions has its own order parameter that range over a tremendous
variety of physical properties. These properties include the density of a
liquid gas transition, the magnetization in a ferromagnet, the size of a
connected cluster in a percolation transition, and a condensate wave function
in a superfluid or superconductor. A continuous transition occurs when that
jump approaches zero. This note is about statistical mechanics and the
development of mean field theory as a basis for a partial understanding of this
phenomenon.Comment: 25 pages, 6 figure
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