10,820 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
Wigner function for a particle in an infinite lattice
We study the Wigner function for a quantum system with a discrete, infinite
dimensional Hilbert space, such as a spinless particle moving on a one
dimensional infinite lattice. We discuss the peculiarities of this scenario and
of the associated phase space construction, propose a meaningful definition of
the Wigner function in this case, and characterize the set of pure states for
which it is non-negative. We propose a measure of non-classicality for states
in this system which is consistent with the continuum limit. The prescriptions
introduced here are illustrated by applying them to localized and Gaussian
states, and to their superpositions.Comment: 19 pages (single column), 7 figure
Towards a wave theory of charged beam transport: A collection of thoughts
We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport
Comment on "Typicality for Generalized Microcanonical Ensemble"
The validity of the so-called "typicality" argument for a generalised
microcanonical ensemble proposed recently is examined.Comment: Version to appear in PR
How much entanglement is needed to reduce the energy variance?
We explore the relation between the entanglement of a pure state and its
energy variance for a local one dimensional Hamiltonian, as the system size
increases. In particular, we introduce a construction which creates a matrix
product state of arbitrarily small energy variance for spins,
with bond dimension scaling as , where is a
constant. This implies that a polynomially increasing bond dimension is enough
to construct states with energy variance that vanishes with the inverse of the
logarithm of the system size. We run numerical simulations to probe the
construction on two different models, and compare the local reduced density
matrices of the resulting states to the corresponding thermal equilibrium. Our
results suggest that the spatially homogeneous states with logarithmically
decreasing variance, which can be constructed efficiently, do converge to the
thermal equilibrium in the thermodynamic limit, while the same is not true if
the variance remains constant.Comment: small changes to fix typos and bibliographic reference
Optimal fidelity of teleportation of coherent states and entanglement
We study the Braunstein-Kimble protocol for the continuous variable
teleportation of a coherent state. We determine lower and upper bounds for the
optimal fidelity of teleportation, maximized over all local Gaussian operations
for a given entanglement of the two-mode Gaussian state shared by the sender
(Alice) and the receiver (Bob). We also determine the optimal local
transformations at Alice and Bob sites and the corresponding maximum fidelity
when one restricts to local trace-preserving Gaussian completely positive maps.Comment: 10 pages, 2 figure
A Double Classification of Common Pitfalls in Ontologies
The application of methodologies for building ontologies has improved the ontology quality. However, such a quality is not totally guaranteed because of the difficulties involved in ontology modelling. These difficulties are related to the inclusion of anomalies or worst practices in the modelling. In this context, our aim in this paper is twofold: (1) to provide a catalogue of common worst practices, which we call pitfalls, and (2) to present a double classification of such pitfalls. These two products will serve in the ontology development in two ways: (a) to avoid the appearance of pitfalls in the ontology modelling, and (b) to evaluate and correct ontologies to improve their quality
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