1,948 research outputs found
Non-negative Wigner functions in prime dimensions
According to a classical result due to Hudson, the Wigner function of a pure,
continuous variable quantum state is non-negative if and only if the state is
Gaussian. We have proven an analogous statement for finite-dimensional quantum
systems. In this context, the role of Gaussian states is taken on by stabilizer
states. The general results have been published in [D. Gross, J. Math. Phys.
47, 122107 (2006)]. For the case of systems of odd prime dimension, a greatly
simplified proof can be employed which still exhibits the main ideas. The
present paper gives a self-contained account of these methods.Comment: 5 pages. Special case of a result proved in quant-ph/0602001. The
proof is greatly simplified, making the general case more accessible. To
appear in Appl. Phys. B as part of the proceedings of the 2006 DPG Spring
Meeting (Quantum Optics and Photonics section
Localization of Multi-Dimensional Wigner Distributions
A well known result of P. Flandrin states that a Gaussian uniquely maximizes
the integral of the Wigner distribution over every centered disc in the phase
plane. While there is no difficulty in generalizing this result to
higher-dimensional poly-discs, the generalization to balls is less obvious. In
this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic
Uniqueness results for the phase retrieval problem of fractional Fourier transforms of variable order
In this paper, we investigate the uniqueness of the phase retrieval problem
for the fractional Fourier transform (FrFT) of variable order. This problem
occurs naturally in optics and quantum physics. More precisely, we show that if
and are such that fractional Fourier transforms of order have
same modulus for some set of 's,
then is equal to up to a constant phase factor. The set depends
on some extra assumptions either on or on both and . Cases
considered here are , of compact support, pulse trains, Hermite
functions or linear combinations of translates and dilates of Gaussians. In
this last case, the set may even be reduced to a single point (i.e. one
fractional Fourier transform may suffice for uniqueness in the problem)
Localizability in de Sitter space
An analogue of the Newton-Wigner position operator is defined for a massive
neutral scalar field in de Sitter space. The one-particle subspace of the
theory, consisting of positive-energy solutions of the Klein-Gordon equation
selected by the Hadamard condition, is identified with an irreducible
representation of de Sitter group. Postulates of localizability analogous to
those written by Wightman for fields in Minkowski space are formulated on it,
and a unique solution is shown to exist. A simple expression for the
time-evolution of the operator is presented.Comment: Presentation improved; references adde
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