Process estimation in the presence of time-invariant memory effects

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.

Quantum estimation via sequential measurements

“…Accordingly, as long as S * á ñ exhibits a nontrivial functional dependence upon g, the Fisher information g ( )  increases linearly in N, yielding an estimation error (22) which diminishes as g N 1 d  (in (23) we have omitted the contribution from g s ¶ ¶ to the Fisher information g ( )  since it does not grow with N). It may happen however that the quantity S * á ñ does not depend upon g. In such a case g ( )  nullifies, signaling that it is impossible to recover g through S (a problem which cannot be fixed by properly choosing the input state 0 r of the probe, the asymptotic distribution (21) being independent of 0 r ).…”

“…Various schemes for quantum parameter estimation based on repetitive or continuous measurements have been studied: see e.g. [17][18][19][20][21][22][23][24][25]. Among them, analogous setups were analyzed in [19,24], where the problem was formalized in terms of quantum Markov chains.…”

Quantum process identification: a method for characterizing non-markovian quantum dynamics

“…For our final case study, we considered a P 31 donor in 28 Si with 29 Si impurities. The nuclear spin of the P 31 defines a qubit.…”

“…As will be explained, our method for identifying quantum processes is based on a classic technique for reconstructing classical discrete-time linear systems from time traces, a technique also utilized in [27] for Markovian quantum processes. [19,20,28,29] also present general frameworks for representing and characterizing non-Markovian quantum dynamics, but address slightly different situations than QPI and employ rather different formalisms. [28,29] consider quantum communication channels with memory, wherein the system is prepared afresh for each use of the channel; in QPI, each occurrence of the process in question begins with the state resulting from the preceding occurrence, a model more appropriate in computing contexts.…”

“…[19,20,28,29] also present general frameworks for representing and characterizing non-Markovian quantum dynamics, but address slightly different situations than QPI and employ rather different formalisms. [28,29] consider quantum communication channels with memory, wherein the system is prepared afresh for each use of the channel; in QPI, each occurrence of the process in question begins with the state resulting from the preceding occurrence, a model more appropriate in computing contexts. [20] considers controlled operations on a system interleaved with system-environment interactions and presents a way to determine a tensor that relates fixed-length control sequences to resulting system states.…”