89 research outputs found
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
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
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
Physics as Information Processing
I review some recent advances in foundational research at Pavia QUIT group.
The general idea is that there is only Quantum Theory without quantization
rules, and the whole Physics---including space-time and relativity--is emergent
from the quantum-information processing. And since Quantum Theory itself is
axiomatized solely on informational principles, the whole Physics must be
reformulated in information-theoretical terms: this is the "It from Bit of J.
A. Wheeler. The review is divided into four parts: a) the informational
axiomatization of Quantum Theory; b) how space-time and relativistic covariance
emerge from quantum computation; c) what is the information-theoretical meaning
of inertial mass and of , and how the quantum field emerges; d) an
observational consequence of the new quantum field theory: a mass-dependent
refraction index of vacuum. I will conclude with the research lines that will
follow in the immediate future.Comment: Work presented at the conference "Advances in Quantum Theory" held on
14-17 June 2010 at the Linnaeus University, Vaxjo, Swede
Operational axioms for C*-algebra representation of transformations
It is shown how a C*-algebra representation of the transformations of a
physical system can be derived from two operational postulates: 1) the
existence of dynamically independent systems}; 2) the existence of symmetric
faithful states. Both notions are crucial for the possibility of performing
experiments on the system, in preventing remote instantaneous influences and in
allowing calibration of apparatuses. The case of Quantum Mechanics is
thoroughly analyzed. The possibility that other no-signaling theories admit a
C*-algebra formulation is discussed.Comment: Work presented at the conference {\em Quantum Theory: Reconsideration
of Foundations, 4} held on 11-16 June 2007 at the International Centre for
Mathematical Modeling in Physics, Engineering and Cognitive Sciences, Vaxjo
University, Swede
On the Heisenberg principle, namely on the information-disturbance trade-off in a quantum measurement
Common misconceptions on the Heisenberg principle are reviewed, and the
original spirit of the principle is reestablished in terms of the trade-off
between information retrieved by a measurement and disturbance on the measured
system. After analyzing the possibility of probabilistically reversible
measurements, along with erasure of information and undoing of disturbance,
general information-disturbance trade-offs are presented, where the disturbance
of the measurement is related to the possibility in principle of undoing its
effect.Comment: 13 LeTeX pages, 2 figures, fortschritte.sty. To appear on
Fortschritte der Physik. Presented at Quantum Interferometry IV, Trieste,
March 200
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