Process estimation in presence of time-invariant memory effects

TL;DR

This paper introduces a novel estimation method to characterize quantum memory effects in systems where traditional methods fail due to internal memory, revealing observable patterns that encode the memory channels without direct access.

Contribution

It presents a new approach to uncover quantum memory interactions from data sequences, even when memory degrees are inaccessible, and demonstrates its effectiveness for qubit memory channels.

Findings

Memory channels generated by controlled unitaries are indistinguishable from memoryless channels.

The method uncovers complete information about the memory channels from observable data.

The approach works despite the failure of standard memoryless quantum process tomography.

Abstract

Any repeated use of a fixed experimental instrument is subject to memory effects. We design an estimation method uncovering the details of the underlying interaction between the system and the internal memory without having any experimental access to memory degrees of freedom. In such case, by definition, any memoryless quantum process tomography (QPT) fails, because the observed data sequences do not satisfy the elementary condition of statistical independence. However, we show that the randomness implemented in certain QPT schemes is sufficient to guarantee the emergence of observable "statistical" patterns containing complete information on the memory channels. We demonstrate the algorithm in details for case of qubit memory channels with two-dimensional memory. Interestingly, we found that for arbitrary estimation method the memory channels generated by controlled unitary interactions are indistinguishable from memoryless unitary channels.