Markovianization with approximate unitary designs

Pedro Figueroa–Romero,Felix A Pollock,Kavan Modi

doi:10.1038/s42005-021-00629-w

Pedro Figueroa–Romero, Felix A Pollock + Show 1 more

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https://doi.org/10.1038/s42005-021-00629-w

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Journal: Communications Physics	Publication Date: Jun 9, 2021
Citations: 10	License type: open-access

Affiliation: Monash University

Abstract

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the environment forgetful. Here we prove that there are physical non-Markovian processes that with high probability look highly Markovian for all orders of correlations; we call this phenomenon Markovianization. Formally, we show that when a quantum process has dynamics given by an approximate unitary design, a large deviation bound on the size of non-Markovian memory is implied. We exemplify our result employing an efficient construction of an approximate unitary circuit design using two-qubit interactions only, showing how seemingly simple systems can speedily become forgetful. Conversely, since the process is closed, it should be possible to detect the underlying non-Markovian effects. However, for these processes, observing non-Markovian signatures would require highly entangling resources and hence be a difficult task.

Highlights

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm
The dynamical version of this conundrum concerns the emergence of forgetful processes from isolated ones
For finite-sized environments, this can only be achieved exactly by continually refreshing the environment’s state, i.e., artificially throwing away information from the environment. The problem this poses is akin to the one made by the Fundamental Postulate of Statistical Mechanics[1], which a-priori sets the probabilities of a closed system to be in any of its accessible microstates as equal

Summary

Introduction

Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. We show that when a quantum process has dynamics given by an approximate unitary design, a large deviation bound on the size of non-Markovian memory is implied. A carbon atom does not typically remember its past and behaves like any other carbon atom Such processes are not isolated, and the general intuition is that the dynamics of a system, in contact with a large environment, can be approximately described as memoryless[2]. As a proof of principle, we employ a recent efficient construction of approximate unitary designs with quantum circuits[14] to illustrate how a dilute gas would quickly Markovianize These results directly impose bounds on complexity and timescales for standard master equations employed in the theory of open systems. Our results are timely given the ever-increasing interest and relevance in determining the breakdown of the Markovian approximation in modern experiments[15,16,17,18]

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