794 research outputs found
Kochen-Specker theorem and experimental test on hidden variables
A recent proposal to experimentally test quantum mechanics against
noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is
shown to be related with the smallest proof of the Kochen-Specker theorem
currently known [Phys. Lett. A 212, 183 (1996)]. This proof contains eighteen
yes-no questions about a four-dimensional physical system, combined in nine
mutually incompatible tests. When these tests are considered as tests about a
two-part two-state system, then quantum mechanics and non-contextual hidden
variables make the same predictions for eight of them, but make different
predictions for the ninth. Therefore, this ninth test would allow us to
discriminate between quantum mechanics and noncontextual hidden-variable
theories in a (gedanken) single run experiment.Comment: 4 pages, 1 figure. To appear in Int. J. Mod. Phys.
Alice and Bob get away with it: A playlet
Alice and Bob use Aravind's version of the Bell-Kochen-Specker theorem to fend off awkward questions about what exactly they were doing in Amsterdam last week
Proposed test of macroscopic quantum contextuality
We show that, for any system with a number of levels which can be identified
with n qubits, there is an inequality for the correlations between three
compatible dichotomic measurements which must be satisfied by any noncontextual
theory, but is violated by any quantum state. Remarkably, the violation grows
exponentially with n, and the tolerated error per correlation also increases
with n, showing that state-independent quantum contextuality is experimentally
observable in complex systems.Comment: REVTeX4, 5 pages, 1 figur
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.
Entropic Test of Quantum Contextuality
We study the contextuality of a three-level quantum system using classical
conditional entropy of measurement outcomes. First, we analytically construct
the minimal configuration of measurements required to reveal contextuality.
Next, an entropic contextual inequality is formulated, analogous to the
entropic Bell inequalities derived by Braunstein and Caves in [Phys. Rev. Lett.
{\bf 61}, 662 (1988)], that must be satisfied by all non-contextual theories.
We find optimal measurements for violation of this inequality. The approach is
easily extendable to higher dimensional quantum systems and more measurements.
Our theoretical findings can be verified in the laboratory with current
technology.Comment: 4 pages, 4 figure
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
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
Quantum contextuality in N-boson systems
Quantum contextuality in systems of identical bosonic particles is explicitly
exhibited via the maximum violation of a suitable inequality of
Clauser-Horne-Shimony-Holt type. Unlike the approaches considered so far, which
make use of single-particle observables, our analysis involves collective
observables constructed using multi-boson operators. An exemplifying scheme to
test this violation with a quantum optical setup is also discussed.Comment: 4 pages, 1 figure, LaTe
Twin inequality for fully contextual quantum correlations
Quantum mechanics exhibits a very peculiar form of contextuality. Identifying
and connecting the simplest scenarios in which more general theories can or
cannot be more contextual than quantum mechanics is a fundamental step in the
quest for the principle that singles out quantum contextuality. The former
scenario corresponds to the Klyachko-Can-Binicioglu-Shumovsky (KCBS)
inequality. Here we show that there is a simple tight inequality, twin to the
KCBS, for which quantum contextuality cannot be outperformed. In a sense, this
twin inequality is the simplest tool for recognizing fully contextual quantum
correlations.Comment: REVTeX4, 4 pages, 1 figur
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
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