40 research outputs found
Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments
If noncontextuality is defined as the robustness of a system's response to a
measurement against other simultaneous measurements, then the Kochen-Specker
arguments do not provide an algebraic proof for quantum contextuality. Namely,
for the argument to be effective, (i) each operator must be uniquely associated
with a measurement and (ii) commuting operators must represent simultaneous
measurements. However, in all Kochen-Specker arguments discussed in the
literature either (i) or (ii) is not met. Arguments meeting (i) contain at
least one subset of mutually commuting operators which do not represent
simultaneous measurements and hence fail to physically justify the functional
composition principle. Arguments meeting (ii) associate some operators with
more than one measurement and hence need to invoke an extra assumption
different from noncontextuality.Comment: 27 pages, 1 figur
Bell inequality and common causal explanation in algebraic quantum field theory
Bell inequalities, understood as constraints between classical conditional
probabilities, can be derived from a set of assumptions representing a common
causal explanation of classical correlations. A similar derivation, however, is
not known for Bell inequalities in algebraic quantum field theories
establishing constraints for the expectation of specific linear combinations of
projections in a quantum state. In the paper we address the question as to
whether a 'common causal justification' of these non-classical Bell
inequalities is possible. We will show that although the classical notion of
common causal explanation can readily be generalized for the non-classical
case, the Bell inequalities used in quantum theories cannot be derived from
these non-classical common causes. Just the opposite is true: for a set of
correlations there can be given a non-classical common causal explanation even
if they violate the Bell inequalities. This shows that the range of common
causal explanations in the non-classical case is wider than that restricted by
the Bell inequalities
EPR correlations, Bell inequalities and common cause systems
Standard common causal explanations of the EPR situation assume a so-called joint common cause system that is a common cause for all correlations. However, the assumption of a joint common cause system together with some other physically motivated assumptions concerning locality and no-conspiracy results in various Bell inequalities. Since Bell inequalities are violated for appropriate measurement settings, a local, non-conspiratorial joint common causal explanation of the EPR situation is ruled out. But why do we assume that a common causal explanation of a set of correlation consists in finding a joint common cause system for all correlations and not just in finding separate common cause systems for the different correlations? What are the
perspectives of a local, non-conspiratorial separate common causal explanation for the EPR scenario? And finally, how do Bell inequalities relate to the weaker assumption of separate common cause systems
On the relation between the probabilistic characterization of the common cause and Bell's notion of local causality
In the paper the relation between the standard probabilistic
characterization of the common cause (used for the derivation of the Bell inequalities) and Bell's notion of local causality will be investigated. It will be shown that the probabilistic common cause follows from local causality if one accepts, as Bell did, two assumptions concerning the
common cause: first, the common cause is localized in the intersection of the past of the correlating events; second, it provides a complete specification of the `beables' of this intersection. However, neither assumptions are a priori requirements. In the paper the logical role of these assumptions will be studied and it will be shown that only the second assumption is necessary for the derivation of the probabilistic common cause from local causality
Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments
If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality
Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments
If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality
Bell's local causality is a d-separation criterion
This paper aims to motivate Bell's notion of local causality by means of
Bayesian networks. In a locally causal theory any superluminal correlation
should be screened off by atomic events localized in any so-called
\textit{shielder-off region} in the past of one of the correlating events. In a
Bayesian network any correlation between non-descendant random variables are
screened off by any so-called \textit{d-separating set} of variables. We will
argue that the shielder-off regions in the definition of local causality
conform in a well defined sense to the d-separating sets in Bayesian networks.Comment: 13 pages, 8 figure