851 research outputs found
Adaptive Bayesian and frequentist data processing for quantum tomography
The outcome statistics of an informationally complete quantum measurement for
a system in a given state can be used to evaluate the ensemble expectation of
any linear operator in the same state, by averaging a function of the outcomes
that depends on the specific operator. Here we introduce two novel
data-processing strategies, non-linear in the frequencies, which lead to faster
convergence to theoretical expectations.Comment: 12 pages, 2 figures, revised versio
Orthogonality relations in Quantum Tomography
Quantum estimation of the operators of a system is investigated by analyzing
its Liouville space of operators. In this way it is possible to easily derive
some general characterization for the sets of observables (i.e. the possible
quorums) that are measured for the quantum estimation. In particular we analyze
the reconstruction of operators of spin systems.Comment: 10 pages, 2 figure
On the realization of Bell observables
We show how Bell observables on a bipartite quantum system can be obtained by
local observables via a controlled-unitary transformation. For continuous
variables this result holds for the Bell observable corresponding to the
non-conventional heterodyne measurement on two radiation modes, which is
connected through a 50-50 beam-splitter to two local observables given by
single-mode homodyne measurements. A simple scheme for a controlled-unitary
transformation of continuous variables is also presented, which needs only two
squeezers, a parametric downconverter and two beam splitters.Comment: 9 pages, elsart, 1 figur
Added noise in homodyne measurement of field-observables
Homodyne tomography provides a way for measuring generic field-operators.
Here we analyze the determination of the most relevant quantities: intensity,
field, amplitude and phase. We show that tomographic measurements are affected
by additional noise in comparison with the direct detection of each observable
by itself. The case of of coherent states has been analyzed in details and
earlier estimations of tomographic precision are critically discussed.Comment: Two figures. Submitted to Phys. Lett.
Extremal covariant quantum operations and POVM's
We consider the convex sets of QO's (quantum operations) and POVM's (positive
operator valued measures) which are covariant under a general
finite-dimensional unitary representation of a group. We derive necessary and
sufficient conditions for extremality, and give general bounds for ranks of the
extremal POVM's and QO's. Results are illustrated on the basis of simple
examples.Comment: 18 pages, to appear on J. Math. Phy
No-signaling, dynamical independence, and the local observability principle
Within a general operational framework I show that a-causality at a distance
of "local actions" (the so-called "no-signaling") is a direct consequence of
commutativity of local transformations, i.e. of dynamical independence. On the
other hand, the tensor product of Quantum Mechanics is not just a consequence
of such dynamical independence, but needs in addition the Local Observability
Principle.Comment: Presented at the conference "Theory and Technology in Quantum
Information, Communication, Computation and Cryptography", Trieste SISSA,
June 2006. Submitted to J. Phys. A. Math. Ge
Physics as Quantum Information Processing: Quantum Fields as Quantum Automata
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can
physics be simulated by a quantum computer? Do we believe that a quantum field
is ultimately made of a numerable set of quantum systems that are unitarily
interacting? A positive answer to these questions corresponds to substituting
QFT with a theory of quantum cellular automata (QCA), and the present work is
examining this hypothesis. These investigations are part of a large research
program on a "quantum-digitalization" of physics, with Quantum Theory as a
special theory of information, and Physics as emergent from the same
quantum-information processing. A QCA-based QFT has tremendous potential
advantages compared to QFT, being quantum "ab-initio" and free from the
problems plaguing QFT due to the continuum hypothesis. Here I will show how
dynamics emerges from the quantum processing, how the QCA can reproduce the
Dirac-field phenomenology at large scales, and the kind of departures from QFT
that that should be expected at a Planck-scale discreteness. I will introduce
the notions of linear field quantum automaton and local-matrix quantum
automaton, in terms of which I will provide the solution to the Feynman's
problem about the possibility of simulating a Fermi field with a quantum
computer.Comment: This version: further improvements in notation. Added reference. Work
presented at the conference "Foundations of Probability and Physics-6" (FPP6)
held on 12-15 June 2011 at the Linnaeus University, Vaaxjo, Sweden. Many new
results, e.g. Feynman problem of qubit-ization of Fermi fields solved
Operational Axioms for Quantum Mechanics
The mathematical formulation of Quantum Mechanics in terms of complex Hilbert
space is derived for finite dimensions, starting from a general definition of
"physical experiment" and from five simple Postulates concerning "experimental
accessibility and simplicity". For the infinite dimensional case, on the other
hand, a C*-algebra representation of physical transformations is derived,
starting from just four of the five Postulates via a Gelfand-Naimark-Segal
(GNS) construction. The present paper simplifies and sharpens the previous
derivation in version 1. The main ingredient of the axiomatization is the
postulated existence of "faithful states" that allows one to calibrate the
experimental apparatus. Such notion is at the basis of the operational
definitions of the scalar product and of the "transposed" of a physical
transformation. What is new in the present paper with respect to
quant-ph/0603011 is the operational deduction of an involution corresponding to
the "complex-conjugation" for effects, whose extension to transformations
allows to define the "adjoint" of a transformation when the extension is
composition-preserving.Comment: New improvements have been made. Work presented at the conference
"Foundations of Probability and Physics-4, Quantum Theory: Reconsideration of
Foundations-3" held on 4-9 June at the International Centre for Mathematical
Modelling in Physics, Engineering and Cognitive Sciences, Vaxjo University,
Sweden. Also contains an errata to "How to Derive the Hilbert-Space
Formulation of Quantum Mechanics From Purely Operational Axioms",
quant-ph/060301
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