1,016 research outputs found
Positive Wigner functions render classical simulation of quantum computation efficient
We show that quantum circuits where the initial state and all the following
quantum operations can be represented by positive Wigner functions can be
classically efficiently simulated. This is true both for continuous-variable as
well as discrete variable systems in odd prime dimensions, two cases which will
be treated on entirely the same footing. Noting the fact that Clifford and
Gaussian operations preserve the positivity of the Wigner function, our result
generalizes the Gottesman-Knill theorem. Our algorithm provides a way of
sampling from the output distribution of a computation or a simulation,
including the efficient sampling from an approximate output distribution in
case of sampling imperfections for initial states, gates, or measurements. In
this sense, this work highlights the role of the positive Wigner function as
separating classically efficiently simulatable systems from those that are
potentially universal for quantum computing and simulation, and it emphasizes
the role of negativity of the Wigner function as a computational resource.Comment: 7 pages, minor change
Quantum repeated games
In a two-stage repeated classical game of prisoners' dilemma the knowledge
that both players will defect in the second stage makes the players to defect
in the first stage as well. We find a quantum version of this repeated game
where the players decide to cooperate in the first stage while knowing that
both will defect in the second.Comment: Revised in the light of referee's comments. Latex, 10 pages, 1 eps
figure, submitted to Physics Letters
On the experimental feasibility of continuous-variable optical entanglement distillation
Entanglement distillation aims at preparing highly entangled states out of a
supply of weakly entangled pairs, using local devices and classical
communication only. In this note we discuss the experimentally feasible schemes
for optical continuous-variable entanglement distillation that have been
presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A
67, 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio,
Annals of Physics (NY) 311, 431 (2004)]. We emphasize their versatility in
particular with regards to the detection process and discuss the merits of the
two proposed detection schemes, namely photo-detection and homodyne detection,
in the light of experimental realizations of this idea becoming more and more
feasible.Comment: 5 pages, 5 figures, contribution to conference proceeding
Rates of multi-partite entanglement transformations and applications in quantum networks
The theory of the asymptotic manipulation of pure bipartite quantum systems
can be considered completely understood: The rates at which bipartite entangled
states can be asymptotically transformed into each other are fully determined
by a single number each, the respective entanglement entropy. In the
multi-partite setting, similar questions of the optimally achievable rates of
transforming one pure state into another are notoriously open. This seems
particularly unfortunate in the light of the revived interest in such questions
due to the perspective of experimentally realizing multi-partite quantum
networks. In this work, we report substantial progress by deriving surprisingly
simple upper and lower bounds on the rates that can be achieved in asymptotic
multi-partite entanglement transformations. These bounds are based on ideas of
entanglement combing and state merging. We identify cases where the bounds
coincide and hence provide the exact rates. As an example, we bound rates at
which resource states for the cryptographic scheme of quantum secret sharing
can be distilled from arbitrary pure tripartite quantum states, providing
further scope for quantum internet applications beyond point-to-point.Comment: 4+7 pages, 1 figure, v2 is significantly extended in its results and
presents a general statement providing bounds for achievable asymptotic rates
for an arbitrary number of partie
Optimal entanglement witnesses for continuous-variable systems
This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update
Novel schemes for measurement-based quantum computation
We establish a framework which allows one to construct novel schemes for
measurement-based quantum computation. The technique further develops tools
from many-body physics - based on finitely correlated or projected entangled
pair states - to go beyond the cluster-state based one-way computer. We
identify resource states that are radically different from the cluster state,
in that they exhibit non-vanishing correlation functions, can partly be
prepared using gates with non-maximal entangling power, or have very different
local entanglement properties. In the computational models, the randomness is
compensated in a different manner. It is shown that there exist resource states
which are locally arbitrarily close to a pure state. Finally, we comment on the
possibility of tailoring computational models to specific physical systems as,
e.g. cold atoms in optical lattices.Comment: 5 pages RevTeX, 1 figure, many diagrams. Title changed, presentation
improved, material adde
Continuous matrix product state tomography of quantum transport experiments
In recent years, a close connection between the description of open quantum
systems, the input-output formalism of quantum optics, and continuous matrix
product states in quantum field theory has been established. So far, however,
this connection has not been extended to the condensed-matter context. In this
work, we substantially develop further and apply a machinery of continuous
matrix product states (cMPS) to perform tomography of transport experiments. We
first present an extension of the tomographic possibilities of cMPS by showing
that reconstruction schemes do not need to be based on low-order correlation
functions only, but also on low-order counting probabilities. We show that
fermionic quantum transport settings can be formulated within the cMPS
framework. This allows us to present a reconstruction scheme based on the
measurement of low-order correlation functions that provides access to
quantities that are not directly measurable with present technology. Emblematic
examples are high-order correlations functions and waiting times distributions
(WTD). The latter are of particular interest since they offer insights into
short-time scale physics. We demonstrate the functioning of the method with
actual data, opening up the way to accessing WTD within the quantum regime.Comment: 11 pages, 4 figure
Quantum field tomography
We introduce the concept of quantum field tomography, the efficient and
reliable reconstruction of unknown quantum fields based on data of correlation
functions. At the basis of the analysis is the concept of continuous matrix
product states, a complete set of variational states grasping states in quantum
field theory. We innovate a practical method, making use of and developing
tools in estimation theory used in the context of compressed sensing such as
Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum
field states based on low-order correlation functions. In the absence of a
phase reference, we highlight how specific higher order correlation functions
can still be predicted. We exemplify the functioning of the approach by
reconstructing randomised continuous matrix product states from their
correlation data and study the robustness of the reconstruction for different
noise models. We also apply the method to data generated by simulations based
on continuous matrix product states and using the time-dependent variational
principle. The presented approach is expected to open up a new window into
experimentally studying continuous quantum systems, such as encountered in
experiments with ultra-cold atoms on top of atom chips. By virtue of the
analogy with the input-output formalism in quantum optics, it also allows for
studying open quantum systems.Comment: 31 pages, 5 figures, minor change
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