Temporal Leggett-Garg-Bell inequalities for sequential multi-time actions in quantum information processing, and a re-definition of Macroscopic Realism

The usual formulation of Macrorealism is recast to make this notion fully concurrent with the basic ideas behind classical physics. The assumption of non-invasiveness of measurements is dropped. Instead, it is assumed that the current state of the system defines full initial conditions for its subsequent evolution. An example of a new family of temporal Bell inequalities is derived which can be applied to processes in which the state of the system undergoes arbitrarily many transformations (which was not the case in the original approach). An exponential (in terms of number of operations) violation of this inequality is demonstrated theoretically. Finally it is shown that such inequalities were indirectly tested in a 2005 experiment by the Weinfurter group.