Experimental Demonstration of Quantum Processes with Finite Memory

Physical systems are inevitably coupled to their environment, leading to memory effects that influence observed statistics; the duration, strength and structure of which are crucial properties of the evolution. Due to the invasive nature of measurement, such properties must be defined with respect to the instruments used to probe the dynamics. Using a photonic platform, we experimentally demonstrate the necessity of describing quantum memory properties in an instrument-specific manner via two paradigmatic processes: the first has finite memory with respect to a quantum measurement; the second, a noisy classical measurement. The former example highlights that future-history correlations can be deterministically erased via quantum measurement, whereas the latter distinguishes quantum from classical measurements: although the classical measurement blocks the history, the process exhibits temporal correlations for more general quantum interrogations. Our methods are relevant to constructing processes with desired memory structures, as required to develop efficient quantum technologies.