102 research outputs found
Does The Uncertainty Relation Determine The Quantum State?
The example of nonpositive trace-class Hermitian operator for which
Robertson-Schroedinger uncertainty relation is fulfilled is presented. The
partial scaling criterion of separability of multimode continuous variable
system is discussed in the context of using nonpositive maps of density
matrices.Comment: 11 pages, to be submitted to Physics Letters
Partial positive scaling transform: a separability criterion
The problem of constructing a necessary and sufficient condition for
establishing the separability of continuous variable systems is revisited.
Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)] pointed out that such a
criterion may be constructed by drawing a parallel between the Peres' partial
transpose criterion for finite dimensional systems and partial time reversal
transformation for continuous variable systems. We generalize the partial time
reversal transformation to a partial scaling transformation and re-examine the
problem using a tomographic description of the continuous variable quantum
system. The limits of applicability of the entanglement criteria obtained from
partial scaling and partial time reversal are explored.Comment: Submitted for publication to Phys. Lett.
Unital quantum operators on the Bloch ball and Bloch region
For one qubit systems, we present a short, elementary argument characterizing
unital quantum operators in terms of their action on Bloch vectors. We then
show how our approach generalizes to multi-qubit systems, obtaining
inequalities that govern when a ``diagonal'' superoperator on the Bloch region
is a quantum operator. These inequalities are the n-qubit analogue of the
Algoet-Fujiwara conditions. Our work is facilitated by an analysis of
operator-sum decompositions in which negative summands are allowed.Comment: Revised and corrected, to appear in Physical Review
On the meaning and interpretation of Tomography in abstract Hilbert spaces
The mechanism of describing quantum states by standard probability
(tomographic one) instead of wave function or density matrix is elucidated.
Quantum tomography is formulated in an abstract Hilbert space framework, by
means of the identity decompositions in the Hilbert space of hermitian linear
operators, with trace formula as scalar product of operators. Decompositions of
identity are considered with respect to over-complete families of projectors
labeled by extra parameters and containing a measure, depending on these
parameters. It plays the role of a Gram-Schmidt orthonormalization kernel. When
the measure is equal to one, the decomposition of identity coincides with a
positive operator valued measure (POVM) decomposition. Examples of spin
tomography, photon number tomography and symplectic tomography are reconsidered
in this new framework.Comment: Submitted to Phys. Lett.
Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
The tomographic picture of quantum mechanics has brought the description of
quantum states closer to that of classical probability and statistics. On the
other hand, the geometrical formulation of quantum mechanics introduces a
metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure
states. By putting these two aspects together, we show that the Fisher
information metric, both classical and quantum, can be described by means of
the Hermitian tensor on the manifold of pure states.Comment: 8 page
On the tomographic description of classical fields
After a general description of the tomographic picture for classical systems,
a tomographic description of free classical scalar fields is proposed both in a
finite cavity and the continuum. The tomographic description is constructed in
analogy with the classical tomographic picture of an ensemble of harmonic
oscillators. The tomograms of a number of relevant states such as the canonical
distribution, the classical counterpart of quantum coherent states and a new
family of so called Gauss--Laguerre states, are discussed. Finally the
Liouville equation for field states is described in the tomographic picture
offering an alternative description of the dynamics of the system that can be
extended naturally to other fields
Volumes of Compact Manifolds
We present a systematic calculation of the volumes of compact manifolds which
appear in physics: spheres, projective spaces, group manifolds and generalized
flag manifolds. In each case we state what we believe is the most natural scale
or normalization of the manifold, that is, the generalization of the unit
radius condition for spheres. For this aim we first describe the manifold with
some parameters, set up a metric, which induces a volume element, and perform
the integration for the adequate range of the parameters; in most cases our
manifolds will be either spheres or (twisted) products of spheres, or quotients
of spheres (homogeneous spaces).
Our results should be useful in several physical instances, as instanton
calculations, propagators in curved spaces, sigma models, geometric scattering
in homogeneous manifolds, density matrices for entangled states, etc. Some flag
manifolds have also appeared recently as exceptional holonomy manifolds; the
volumes of compact Einstein manifolds appear in String theory.Comment: 26 pages, no figures; updated addresses and bibliography. To be
published in Rep. Math. Phy
Quantum Zeno Dynamics
The evolution of a quantum system undergoing very frequent measurements takes
place in a subspace of the total Hilbert space (quantum Zeno effect). The
dynamical properties of this evolution are investigated and several examples
are considered.Comment: 12 pages, 1 figur
Robustness of raw quantum tomography
We scrutinize the effects of non-ideal data acquisition on the homodyne
tomograms of photon quantum states. The presence of a weight function,
schematizing the effects of the finite thickness of the probing beam or
equivalently noise, only affects the state reconstruction procedure by a
normalization constant. The results are extended to a discrete mesh and show
that quantum tomography is robust under incomplete and approximate knowledge of
tomograms.Comment: 7 pages, 1 figure, published versio
f-oscillators deformation for Moyal algebras
Using general construction of star-product the q-deformed Wigner-Weyl-Moyal
quantization procedure is elaborated. The q-deformed Groenewold kernel
determining the product of quantum observables is given in explicit form for
small nonlinearities corresponding to nonlinear vibrations of classical and
quantum q-oscillators. The deformations of Groenewold kernel related to general
kinds of nonlinear vibrations described by f-oscillators are considered.Comment: 11 pages - to be submitted to Physics Letters
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