The quantum theoretical concepts of modular momentum and dynamical non-locality, which were introduced four decades ago, have recently been used to explain single particle quantum interference phenomena. Although the non-local exchange of modular momentum associated with such phenomena cannot be directly observed, it has been suggested that effects induced by this exchange can be measured experimentally using weak measurements of pre-and post-selected ensembles of particles. This paper reports on such an optical experiment that yielded measured weak values that were consistent with the theoretical prediction of an effect induced by a non-local exchange of modular momentum.

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Exact expressions for the mean pointer position, the mean pointer momentum and their variances are obtained for projection operator measurements performed upon ensembles of pre-and postselected (PPS) and preselected-only (PSO) quantum systems. These expressions are valid for any interaction strength which couples a measurement pointer to a quantum system, and consequently should be of general interest to both experimentalists and theoreticians. To account for the 'collapse' of PPS states to PSO states that occurs as interaction strength increases and to introduce the concept of 'weak value persistence', the exact PPS and PSO pointer theories are combined to provide a pointer theory for statistical mixtures. For the purpose of illustrating 'weak value persistence', mixture weights defined in terms of the Bhattacharyya coefficient are used and the statistical mixture theory is applied to mean pointer position data associated with weak value projector measurements obtained from a recent dynamical quantum non-locality detection experiment.

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Straightforward novel methods for stabilizing, tuning, and controlling a twin Mach-Zehnder interferometer for the purpose of observing a subtle dynamical quantum nonlocality effect in a recent optical experiment are presented and discussed. Weak measurements were required for observing a subtle quantum dynamical nonlocality effect that reveals itself in a change of a weak value. Consequently, emphasis is placed upon describing the approaches to apparatus stabilization and interaction strength control between photons and the apparatus. The details discussed in this paper should be of general interest to experimentalists engaging in weak measurement and weak value research.