34,417 research outputs found
Heralded single phonon preparation, storage and readout in cavity optomechanics
We analyze theoretically how to use the radiation pressure coupling between a
mechanical oscillator and an optical cavity field to generate in a heralded way
a single quantum of mechanical motion (a Fock state), and release on-demand the
stored excitation as a single photon. Starting with the oscillator close to its
ground state, a laser pumping the upper motional sideband leads to dynamical
backaction amplification and to the creation of correlated photon-phonon pairs.
The detection of one Stokes photon thus projects the macroscopic oscillator
into a single-phonon Fock state. The non-classical nature of this mechanical
state can be demonstrated by applying a readout laser on the lower sideband
(i.e. optical cooling) to map the phononic state to a photonic mode, and by
performing an autocorrelation measurement on the anti-Stokes photons. We
discuss the relevance of our proposal for the future of cavity optomechanics as
an enabling quantum technology.Comment: Accepted for publication in Physical Review Letters. Added References
42,4
Security of Quantum Key Distribution with Entangled Qutrits
The study of quantum cryptography and quantum non-locality have
traditionnally been based on two-level quantum systems (qubits). In this paper
we consider a generalisation of Ekert's cryptographic protocol [Ekert] where
qubits are replaced by qutrits. The security of this protocol is related to
non-locality, in analogy with Ekert's protocol. In order to study its
robustness against the optimal individual attacks, we derive the information
gained by a potential eavesdropper applying a cloning-based attack.Comment: 9 pages original version: july 2002, replaced in january 2003
(reason: minor changes
Parameter estimation of ODE's via nonparametric estimators
Ordinary differential equations (ODE's) are widespread models in physics,
chemistry and biology. In particular, this mathematical formalism is used for
describing the evolution of complex systems and it might consist of
high-dimensional sets of coupled nonlinear differential equations. In this
setting, we propose a general method for estimating the parameters indexing
ODE's from times series. Our method is able to alleviate the computational
difficulties encountered by the classical parametric methods. These
difficulties are due to the implicit definition of the model. We propose the
use of a nonparametric estimator of regression functions as a first-step in the
construction of an M-estimator, and we show the consistency of the derived
estimator under general conditions. In the case of spline estimators, we prove
asymptotic normality, and that the rate of convergence is the usual
-rate for parametric estimators. Some perspectives of refinements of
this new family of parametric estimators are given.Comment: Published in at http://dx.doi.org/10.1214/07-EJS132 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Cloning a Qutrit
We investigate several classes of state-dependent quantum cloners for
three-level systems. These cloners optimally duplicate some of the four
maximally-conjugate bases with an equal fidelity, thereby extending the
phase-covariant qubit cloner to qutrits. Three distinct classes of qutrit
cloners can be distinguished, depending on two, three, or four
maximally-conjugate bases are cloned as well (the latter case simply
corresponds to the universal qutrit cloner). These results apply to symmetric
as well as asymmetric cloners, so that the balance between the fidelity of the
two clones can also be analyzed.Comment: 14 pages LaTex. To appear in the Journal of Modern Optics for the
special issue on "Quantum Information: Theory, Experiment and Perspectives".
Proceedings of the ESF Conference, Gdansk, July 10-18, 200
Continuous-variable entropic uncertainty relations
Uncertainty relations are central to quantum physics. While they were
originally formulated in terms of variances, they have later been successfully
expressed with entropies following the advent of Shannon information theory.
Here, we review recent results on entropic uncertainty relations involving
continuous variables, such as position and momentum . This includes the
generalization to arbitrary (not necessarily canonically-conjugate) variables
as well as entropic uncertainty relations that take - correlations into
account and admit all Gaussian pure states as minimum uncertainty states. We
emphasize that these continuous-variable uncertainty relations can be
conveniently reformulated in terms of entropy power, a central quantity in the
information-theoretic description of random signals, which makes a bridge with
variance-based uncertainty relations. In this review, we take the quantum
optics viewpoint and consider uncertainties on the amplitude and phase
quadratures of the electromagnetic field, which are isomorphic to and ,
but the formalism applies to all such variables (and linear combinations
thereof) regardless of their physical meaning. Then, in the second part of this
paper, we move on to new results and introduce a tighter entropic uncertainty
relation for two arbitrary vectors of intercommuting continuous variables that
take correlations into account. It is proven conditionally on reasonable
assumptions. Finally, we present some conjectures for new entropic uncertainty
relations involving more than two continuous variables.Comment: Review paper, 42 pages, 1 figure. We corrected some minor errors in
V
Adiabatic quantum search algorithm for structured problems
The study of quantum computation has been motivated by the hope of finding
efficient quantum algorithms for solving classically hard problems. In this
context, quantum algorithms by local adiabatic evolution have been shown to
solve an unstructured search problem with a quadratic speed-up over a classical
search, just as Grover's algorithm. In this paper, we study how the structure
of the search problem may be exploited to further improve the efficiency of
these quantum adiabatic algorithms. We show that by nesting a partial search
over a reduced set of variables into a global search, it is possible to devise
quantum adiabatic algorithms with a complexity that, although still
exponential, grows with a reduced order in the problem size.Comment: 7 pages, 0 figur
Operational quantum theory without predefined time
The standard formulation of quantum theory assumes a predefined notion of
time. This is a major obstacle in the search for a quantum theory of gravity,
where the causal structure of space-time is expected to be dynamical and
fundamentally probabilistic in character. Here, we propose a generalized
formulation of quantum theory without predefined time or causal structure,
building upon a recently introduced operationally time-symmetric approach to
quantum theory. The key idea is a novel isomorphism between transformations and
states which depends on the symmetry transformation of time reversal. This
allows us to express the time-symmetric formulation in a time-neutral form with
a clear physical interpretation, and ultimately drop the assumption of time. In
the resultant generalized formulation, operations are associated with regions
that can be connected in networks with no directionality assumed for the
connections, generalizing the standard circuit framework and the process matrix
framework for operations without global causal order. The possible events in a
given region are described by positive semidefinite operators on a Hilbert
space at the boundary, while the connections between regions are described by
entangled states that encode a nontrivial symmetry and could be tested in
principle. We discuss how the causal structure of space-time could be
understood as emergent from properties of the operators on the boundaries of
compact space-time regions. The framework is compatible with indefinite causal
order, timelike loops, and other acausal structures.Comment: 15 pages, 7 figures, published version (this version covers the
second half of the original submission; the first half has been published
separately and is available at arXiv:1507.07745
Operational formulation of time reversal in quantum theory
The symmetry of quantum theory under time reversal has long been a subject of
controversy because the transition probabilities given by Born's rule do not
apply backward in time. Here, we resolve this problem within a rigorous
operational probabilistic framework. We argue that reconciling time reversal
with the probabilistic rules of the theory requires a notion of operation that
permits realizations via both pre- and post-selection. We develop the
generalized formulation of quantum theory that stems from this approach and
give a precise definition of time-reversal symmetry, emphasizing a previously
overlooked distinction between states and effects. We prove an analogue of
Wigner's theorem, which characterizes all allowed symmetry transformations in
this operationally time-symmetric quantum theory. Remarkably, we find larger
classes of symmetry transformations than those assumed before. This suggests a
possible direction for search of extensions of known physics.Comment: 17 pages, 5 figure
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