Leggett-Garg macrorealism and the quantum nondisturbance conditions. (arXiv:1812.02346v2 [quant-ph] UPDATED)

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.

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