Process estimation in presence of time-invariant memory effects

摘要

Any repeated use of a fixed experimental instrument is subject to memoryeffects. We design an estimation method uncovering the details of theunderlying interaction between the system and the internal memory withouthaving any experimental access to memory degrees of freedom. In such case, bydefinition, any memoryless quantum process tomography (QPT) fails, because theobserved data sequences do not satisfy the elementary condition of statisticalindependence. However, we show that the randomness implemented in certain QPTschemes is sufficient to guarantee the emergence of observable "statistical"patterns containing complete information on the memory channels. We demonstratethe algorithm in details for case of qubit memory channels with two-dimensionalmemory. Interestingly, we found that for arbitrary estimation method the memorychannels generated by controlled unitary interactions are indistinguishablefrom memoryless unitary channels.