2,414 research outputs found
Testing locality and noncontextuality with the lowest moments
The quest for fundamental test of quantum mechanics is an ongoing effort. We
here address the question of what are the lowest possible moments needed to
prove quantum nonlocality and noncontextuality without any further assumption
-- in particular without the often assumed dichotomy. We first show that second
order correlations can always be explained by a classical noncontextual
local-hidden-variable theory. Similar third-order correlations also cannot
violate classical inequalities in general, except for a special state-dependent
noncontextuality. However, we show that fourth-order correlations can violate
locality and state-independent noncontextuality. Finally we obtain a
fourth-order continuous-variable Bell inequality for position and momentum,
which can be violated and might be useful in Bell tests closing all loopholes
simultaneously.Comment: 12 pages, 1 figur
Relativistic invariance of the vacuum
Relativistic invariance of the vacuum is (or follows from) one of the
Wightman axioms which is commonly believed to be true. Without these axioms,
here we present a direct and general proof of continuous relativistic
invariance of all real-time vacuum correlations of fields, not only scattering
(forward in time), based on closed time path formalism. The only assumptions
are basic principles of relativistic quantum field theories: the relativistic
invariance of the Lagrangian, of the form including known interactions
(electromagnetic, weak and strong), and standard rules of quantization. The
proof is in principle perturbative leaving a possibility of spontaneous
violation of invariance. Time symmetry is however manifestly violated.Comment: 13 pages, 5 figures, more about false reports of PRD Editors V.P.
Nair and G.D. Sprouse at http://www.fuw.edu.pl/~abednorz/riv
Some remarks on the Sudakov minoration
In this paper we discuss Sudakov type minoration for the dependent setting.
Sudakov minoration is a well known property first proved for centered Gaussian
processes which states that for well separated points there is a natural lower
bound on the expectation of the supremum of such a process. We generalize this
concept for the dependent setting where we consider log concave random
variables and then discuss methods of proving the property.Comment: 30 page
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