735 research outputs found
On recognizing and formulating mathematical problems
When mathematics is used to help people cope with real-life situations, a three-stage intellectual process is involved. First, a person becomes aware of a problem-situation which stimulates him to generate a problem-statement, a verbal story-problem. This may be in writing, expressed orally, or merely thought and evidenced by other behavior. Second, he transforms the verbal problem-statement into a mathematical formulation. Third, he analyzes this mathematically stated problem into subproblems to which the solution is more immediate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43864/1/11251_2004_Article_BF00052419.pd
Simulating Quantum Mechanics by Non-Contextual Hidden Variables
No physical measurement can be performed with infinite precision. This leaves
a loophole in the standard no-go arguments against non-contextual hidden
variables. All such arguments rely on choosing special sets of
quantum-mechanical observables with measurement outcomes that cannot be
simulated non-contextually. As a consequence, these arguments do not exclude
the hypothesis that the class of physical measurements in fact corresponds to a
dense subset of all theoretically possible measurements with outcomes and
quantum probabilities that \emph{can} be recovered from a non-contextual hidden
variable model. We show here by explicit construction that there are indeed
such non-contextual hidden variable models, both for projection valued and
positive operator valued measurements.Comment: 15 pages. Journal version. Only minor typo corrections from last
versio
Kochen-Specker theorem as a precondition for secure quantum key distribution
We show that (1) the violation of the Ekert 91 inequality is a sufficient
condition for certification of the Kochen-Specker (KS) theorem, and (2) the
violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a
sufficient condition for certification of the KS theorem. Therefore the success
in each QKD protocol reveals the nonclassical feature of quantum theory, in the
sense that the KS realism is violated. Further, it turned out that the Ekert
inequality and the BBM inequality are depictured by distillable entanglement
witness inequalities. Here, we connect the success in these two key
distribution processes into the no-hidden-variables theorem and into witness on
distillable entanglement. We also discuss the explicit difference between the
KS realism and Bell's local realism in the Hilbert space formalism of quantum
theory.Comment: 4 pages, To appear in Phys. Rev.
Networks and Our Limited Information Horizon
In this paper we quantify our limited information horizon, by measuring the
information necessary to locate specific nodes in a network. To investigate
different ways to overcome this horizon, and the interplay between
communication and topology in social networks, we let agents communicate in a
model society. Thereby they build a perception of the network that they can use
to create strategic links to improve their standing in the network. We observe
a narrow distribution of links when the communication is low and a network with
a broad distribution of links when the communication is high.Comment: 5 pages and 5 figure
Negativity and contextuality are equivalent notions of nonclassicality
Two notions of nonclassicality that have been investigated intensively are:
(i) negativity, that is, the need to posit negative values when representing
quantum states by quasiprobability distributions such as the Wigner
representation, and (ii) contextuality, that is, the impossibility of a
noncontextual hidden variable model of quantum theory (also known as the
Bell-Kochen-Specker theorem). Although both of these notions were meant to
characterize the conditions under which a classical explanation cannot be
provided, we demonstrate that they prove inadequate to the task and we argue
for a particular way of generalizing and revising them. With the refined
version of each in hand, it becomes apparent that they are in fact one and the
same. We also demonstrate the impossibility of noncontextuality or
nonnegativity in quantum theory with a novel proof that is symmetric in its
treatment of measurements and preparations.Comment: 5 pages, published version (modulo some supplementary material
A feasible quantum optical experiment capable of refuting noncontextuality for single photons
Elaborating on a previous work by Simon et al. [PRL 85, 1783 (2000)] we
propose a realizable quantum optical single-photon experiment using standard
present day technology, capable of discriminating maximally between the
predictions of quantum mechanics (QM) and noncontextual hidden variable
theories (NCHV). Quantum mechanics predicts a gross violation (up to a factor
of 2) of the noncontextual Bell-like inequality associated with the proposed
experiment. An actual maximal violation of this inequality would demonstrate
(modulo fair sampling) an all-or-nothing type contradiction between QM and
NCHV.Comment: LaTeX file, 8 pages, 1 figur
A Bayesian Analogue of Gleason's Theorem
We introduce a novel notion of probability within quantum history theories
and give a Gleasonesque proof for these assignments. This involves introducing
a tentative novel axiom of probability. We also discuss how we are to interpret
these generalised probabilities as partially ordered notions of preference and
we introduce a tentative generalised notion of Shannon entropy. A Bayesian
approach to probability theory is adopted throughout, thus the axioms we use
will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with
to-be-published versio
Contextuality in Measurement-based Quantum Computation
We show, under natural assumptions for qubit systems, that measurement-based
quantum computations (MBQCs) which compute a non-linear Boolean function with
high probability are contextual. The class of contextual MBQCs includes an
example which is of practical interest and has a super-polynomial speedup over
the best known classical algorithm, namely the quantum algorithm that solves
the Discrete Log problem.Comment: Version 3: probabilistic version of Theorem 1 adde
Comment on ``All quantum observables in a hidden-variable model must commute simultaneously"
Malley discussed {[Phys. Rev. A {\bf 69}, 022118 (2004)]} that all quantum
observables in a hidden-variable model for quantum events must commute
simultaneously. In this comment, we discuss that Malley's theorem is indeed
valid for the hidden-variable theoretical assumptions, which were introduced by
Kochen and Specker. However, we give an example that the local hidden-variable
(LHV) model for quantum events preserves noncommutativity of quantum
observables. It turns out that Malley's theorem is not related with the LHV
model for quantum events, in general.Comment: 3 page
An entropic approach to local realism and noncontextuality
For any Bell locality scenario (or Kochen-Specker noncontextuality scenario),
the joint Shannon entropies of local (or noncontextual) models define a convex
cone for which the non-trivial facets are tight entropic Bell (or
contextuality) inequalities. In this paper we explore this entropic approach
and derive tight entropic inequalities for various scenarios. One advantage of
entropic inequalities is that they easily adapt to situations like bilocality
scenarios, which have additional independence requirements that are non-linear
on the level of probabilities, but linear on the level of entropies. Another
advantage is that, despite the nonlinearity, taking detection inefficiencies
into account turns out to be very simple. When joint measurements are conducted
by a single detector only, the detector efficiency for witnessing quantum
contextuality can be arbitrarily low.Comment: 12 pages, 8 figures, minor mistakes correcte
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