Compatibility and noncontextuality for sequential measurements

A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting "compatibility loophole" and present several methods to rule out certain hidden variable models which obey a kind of extended noncontextuality. Finally, we present a detailed analysis of experimental imperfections in a recent trapped ion experiment and apply our analysis to that case.Comment: 15 pages, 2 figures, v2: problem with latex solve

Leggett-Garg macrorealism and the quantum nondisturbance conditions

We investigate the relation between a refined version of Leggett and Garg conditions for macrorealism, namely the no-signaling-in-time (NSIT) conditions, and the quantum mechanical notion of nondisturbance between measurements. We show that all NSIT conditions are satisfied for any state preparation if and only if certain compatibility criteria on the state-update rules relative to the measurements, i.e. quantum instruments, are met. The systematic treatment of NSIT conditions supported by structural results on nondisturbance provides a unified framework for the discussion of the the clumsiness loophole. This extends previous approaches and allows for a tightening of the loophole via a hierarchy of tests able to disprove a larger class of macrorealist theories. Finally, we discuss perspectives for a resource theory of quantum mechanical disturbance related to violations of macrorealism.Comment: Final versio

Heisenberg's uncertainty principle

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle. (c) 2007 Elsevier B.V. All rights reserved