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The usual formulation of Macrorealism is recast to make this notion fullyconcurrent with the basic ideas behind classical physics. The assumption ofnon-invasiveness of measurements is dropped. Instead, it is assumed that thecurrent state of the system defines full initial conditions for its subsequentevolution. An example of a new family of temporal Bell inequalities is derivedwhich can be applied to processes in which the state of the system undergoesarbitrarily many transformations (which was not the case in the originalapproach). An exponential (in terms of number of operations) violation of thisinequality is demonstrated theoretically. Finally it is shown that suchinequalities were indirectly tested in a 2005 experiment by the Weinfurtergroup.

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