36 research outputs found
Robustness of adiabatic quantum computation
We study the fault tolerance of quantum computation by adiabatic evolution, a
quantum algorithm for solving various combinatorial search problems. We
describe an inherent robustness of adiabatic computation against two kinds of
errors, unitary control errors and decoherence, and we study this robustness
using numerical simulations of the algorithm.Comment: 11 pages, 5 figures, REVTe
Complete positivity and entangled degrees of freedom
We study how some recently proposed noncontextuality tests based on quantum
interferometry are affected if the test particles propagate as open systems in
presence of a gaussian stochastic background. We show that physical consistency
requires the resulting markovian dissipative time-evolution to be completely
positive.Comment: 23 pages, plain-TeX, no figure
Non-Standard neutral kaons dynamics from D-brane statistics
The neutral kaon system can be effectively described by non-unitary,
dissipative, completely positive dynamics that extend the usual treatment. In
the framework of open quantum systems, we show how the origin of these
non-standard time evolutions can be traced to the interaction of the kaon
system with a large environment. We find that D-branes, effectively described
by a heat-bath of quanta obeying infinite statistics, could constitute a
realistic example of such an environment.Comment: 14 pages, plain-TeX, no figure
Automatic Quantum Error Correction
Criteria are given by which dissipative evolution can transfer populations
and coherences between quantum subspaces, without a loss of coherence. This
results in a form of quantum error correction that is implemented by the joint
evolution of a system and a cold bath. It requires no external intervention
and, in principal, no ancilla. An example of a system that protects a qubit
against spin-flip errors is proposed. It consists of three spin 1/2 magnetic
particles and three modes of a resonator. The qubit is the triple quantum
coherence of the spins, and the photons act as ancilla.Comment: 16 pages 12 fig LaTex uses multicol, graphicx expanded version of
letter submitted to Phys Rev Let
Derivation of some translation-invariant Lindblad equations for a quantum Brownian particle
We study the dynamics of a Brownian quantum particle hopping on an infinite
lattice with a spin degree of freedom. This particle is coupled to free boson
gases via a translation-invariant Hamiltonian which is linear in the creation
and annihilation operators of the bosons. We derive the time evolution of the
reduced density matrix of the particle in the van Hove limit in which we also
rescale the hopping rate. This corresponds to a situation in which both the
system-bath interactions and the hopping between neighboring sites are small
and they are effective on the same time scale. The reduced evolution is given
by a translation-invariant Lindblad master equation which is derived
explicitly.Comment: 28 pages, 4 figures, minor revisio
'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion
Recently, several authors studied small quantum systems weakly coupled to
free boson or fermion fields at positive temperature. All the approaches we are
aware of employ complex deformations of Liouvillians or Mourre theory (the
infinitesimal version of the former). We present an approach based on polymer
expansions of statistical mechanics. Despite the fact that our approach is
elementary, our results are slightly sharper than those contained in the
literature up to now. We show that, whenever the small quantum system is known
to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad
equation) in the weak coupling limit, and the Markov approximation is
exponentially mixing, then the weakly coupled system approaches a unique
invariant state that is perturbatively close to its Markov approximation.Comment: 23 pages, v2-->v3: Revised version: The explanatory section 1.7 has
changed and Section 3.2 has been made more explici
Non-commutative Geometry and Kinetic Theory of Open Systems
The basic mathematical assumptions for autonomous linear kinetic equations
for a classical system are formulated, leading to the conclusion that if they
are differential equations on its phase space , they are at most of the 2nd
order. For open systems interacting with a bath at canonical equilibrium they
have a particular form of an equation of a generalized Fokker-Planck type. We
show that it is possible to obtain them as Liouville equations of Hamiltonian
dynamics on with a particular non-commutative differential structure,
provided certain geometric in character, conditions are fulfilled. To this end,
symplectic geometry on is developped in this context, and an outline of the
required tensor analysis and differential geometry is given. Certain questions
for the possible mathematical interpretation of this structure are also
discussed.Comment: 22 pages, LaTe
Open Quantum Dynamics: Complete Positivity and Entanglement
We review the standard treatment of open quantum systems in relation to
quantum entanglement, analyzing, in particular, the behaviour of bipartite
systems immersed in a same environment. We first focus upon the notion of
complete positivity, a physically motivated algebraic constraint on the quantum
dynamics, in relation to quantum entanglement, i.e. the existence of
statistical correlations which can not be accounted for by classical
probability. We then study the entanglement power of heat baths versus their
decohering properties, a topic of increasing importance in the framework of the
fast developing fields of quantum information, communication and computation.
The presentation is self contained and, through several examples, it offers a
detailed survey of the physics and of the most relevant and used techniques
relative to both quantum open system dynamics and quantum entanglement.Comment: LaTex, 77 page
Introduction to decoherence theory
This is an introduction to the theory of decoherence with an emphasis on its
microscopic origins and on a dynamic description. The text corresponds to a
chapter soon to be published in: A. Buchleitner, C. Viviescas, and M. Tiersch
(Eds.), Entanglement and Decoherence. Foundations and Modern Trends, Lecture
Notes in Physics, Vol 768, Springer, Berlin (2009)Comment: 57 pages, 2 figures; some new material added and typos corrected.
This corresponds to the published versio