47 research outputs found
Distillation by repeated measurements: continuous spectrum case
Repeated measurements on a part of a bipartite system strongly affect the
other part not measured, whose dynamics is regulated by an effective contracted
evolution operator. When the spectrum of this operator is discrete, the latter
system is driven into a pure state irrespective of the initial state, provided
the spectrum satisfies certain conditions. We here show that even in the case
of continuous spectrum an effective distillation can occur under rather general
conditions. We confirm it by applying our formalism to a simple model.Comment: 4 pages, 2 figure
Diffusion Approximation of Stochastic Master Equations with Jumps
In the presence of quantum measurements with direct photon detection the
evolution of open quantum systems is usually described by stochastic master
equations with jumps. Heuristically, from these equations one can obtain
diffusion models as approximation. A necessary condition for a general
diffusion approximation for jump master equations is presented. This
approximation is rigorously proved by using techniques for Markov process which
are based upon the convergence of Markov generators and martingale problems.
This result is illustrated by rigorously obtaining the diffusion approximation
for homodyne and heterodyne detection.Comment: 15 page
A Multi-Class SWAP-Test Classifier
Multi-class classification problems are fundamental in many varied domains in
research and industry. To solve multi-class classification problems, heuristic
strategies such as One-vs-One or One-vs-All can be employed. However, these
strategies require the number of binary classification models developed to grow
with the number of classes. Recent work in quantum machine learning has seen
the development of multi-class quantum classifiers that circumvent this growth
by learning a mapping between the data and a set of label states. This work
presents the first multi-class SWAP-Test classifier inspired by its binary
predecessor and the use of label states in recent work. With this classifier,
the cost of developing multiple models is avoided. In contrast to previous
work, the number of qubits required, the measurement strategy, and the topology
of the circuits used is invariant to the number of classes. In addition, unlike
other architectures for multi-class quantum classifiers, the state
reconstruction of a single qubit yields sufficient information for multi-class
classification tasks. Both analytical results and numerical simulations show
that this classifier is not only effective when applied to diverse
classification problems but also robust to certain conditions of noise.Comment: 13 pages, 9 figure
Scaling of non-Markovian Monte Carlo wave-function methods
We demonstrate a scaling method for non-Markovian Monte Carlo wave-function
simulations used to study open quantum systems weakly coupled to their
environments. We derive a scaling equation, from which the result for the
expectation values of arbitrary operators of interest can be calculated, all
the quantities in the equation being easily obtainable from the scaled Monte
Carlo simulations. In the optimal case, the scaling method can be used, within
the weak coupling approximation, to reduce the size of the generated Monte
Carlo ensemble by several orders of magnitude. Thus, the developed method
allows faster simulations and makes it possible to solve the dynamics of the
certain class of non-Markovian systems whose simulation would be otherwise too
tedious because of the requirement for large computational resources.Comment: 10 pages, 3 figures. V2: Minor changes according to the referees'
suggestion
Non-Markovian dynamics of interacting qubit pair coupled to two independent bosonic baths
The dynamics of two interacting spins coupled to separate bosonic baths is
studied. An analytical solution in Born approximation for arbitrary spectral
density functions of the bosonic environments is found. It is shown that in the
non-Markovian cases concurrence "lives" longer or reaches greater values.Comment: 13 page
Parametrizations of density matrices
This article gives a brief overview of some recent progress in the
characterization and parametrization of density matrices of finite dimensional
systems. We discuss in some detail the Bloch-vector and Jarlskog
parametrizations and mention briefly the coset parametrization. As applications
of the Bloch parametrization we discuss the trace invariants for the case of
time dependent Hamiltonians and in some detail the dynamics of three-level
systems. Furthermore, the Bloch vector of two-qubit systems as well as the use
of the polarization operator basis is indicated. As the main application of the
Jarlskog parametrization we construct density matrices for composite systems.
In addition, some recent related articles are mentioned without further
discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and
Conclusion section added, references adde
Non Markovian Quantum Repeated Interactions and Measurements
A non-Markovian model of quantum repeated interactions between a small
quantum system and an infinite chain of quantum systems is presented. By
adapting and applying usual pro jection operator techniques in this context,
discrete versions of the integro-differential and time-convolutioness Master
equations for the reduced system are derived. Next, an intuitive and rigorous
description of the indirect quantum measurement principle is developed and a
discrete non Markovian stochastic Master equation for the open system is
obtained. Finally, the question of unravelling in a particular model of
non-Markovian quantum interactions is discussed.Comment: 22 page
Initial correlations effects on decoherence at zero temperature
We consider a free charged particle interacting with an electromagnetic bath
at zero temperature. The dipole approximation is used to treat the bath
wavelengths larger than the width of the particle wave packet. The effect of
these wavelengths is described then by a linear Hamiltonian whose form is
analogous to phenomenological Hamiltonians previously adopted to describe the
free particle-bath interaction. We study how the time dependence of decoherence
evolution is related with initial particle-bath correlations. We show that
decoherence is related to the time dependent dressing of the particle. Moreover
because decoherence induced by the T=0 bath is very rapid, we make some
considerations on the conditions under which interference may be experimentally
observed.Comment: 16 pages, 1 figur
On the quantum description of Einstein's Brownian motion
A fully quantum treatment of Einstein's Brownian motion is given, showing in
particular the role played by the two original requirements of translational
invariance and connection between dynamics of the Brownian particle and atomic
nature of the medium. The former leads to a clearcut relationship with Holevo's
result on translation-covariant quantum-dynamical semigroups, the latter to a
formulation of the fluctuation-dissipation theorem in terms of the dynamic
structure factor, a two-point correlation function introduced in seminal work
by van Hove, directly related to density fluctuations in the medium and
therefore to its atomistic, discrete nature. A microphysical expression for the
generally temperature dependent friction coefficient is given in terms of the
dynamic structure factor and of the interaction potential describing the single
collisions. A comparison with the Caldeira Leggett model is drawn, especially
in view of the requirement of translational invariance, further characterizing
general structures of reduced dynamics arising in the presence of symmetry
under translations.Comment: 14 pages, latex, no figure