Leggett-Garg macrorealism and the quantum nondisturbance conditions. (arXiv:1812.02346v1 [quant-ph])

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, and obtain a compatibility
relation among an arbitrary number of observables based on their minimally
disturbing sequential implementation. We show that all NSIT conditions are
satisfied for any state preparation if and only if simple compatibility
criteria on the state-update rules relative to the observables, i.e. quantum
instruments, are met. Motivated by this connection, we prove some structural
results on nondisturbance of two or more observables, such as the existence of
noncommuting and two-way nondisturbing observables, and pairwise but not
triplewise nondisturbing observables. Moreover, we discuss perspectives for a
resource theory of quantum disturbance based on the notion of macrorealism by
defining a general measure of disturbance and investigating which operations do
not increase it.

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