# Non-Markovian Memory Strength Bounds Quantum Process Recoverability

## TL;DR

This paper introduces a finite memory approximation for non-Markovian quantum processes, bounding the error by a measurable memory strength, enabling efficient process recovery and analysis.

## Contribution

It proposes a novel finite memory ansatz with error bounds based on operationally defined memory strength, facilitating practical descriptions of complex non-Markovian quantum dynamics.

## Key findings

- Memory truncation is feasible even in highly non-Markovian regimes.
- Recovery error is bounded by the minimal memory strength over all probing methods.
- The approach enables efficient compression and recovery of quantum processes.

## Abstract

Generic non-Markovian quantum processes have infinitely long memory, implying an exact description that grows exponentially in complexity with observation time. Here, we present a finite memory ansatz that approximates (or recovers) the true process with errors bounded by the strength of the non-Markovian memory. The introduced memory strength is an operational quantity and depends on the way the process is probed. Remarkably, the recovery error is bounded by the smallest memory strength over all possible probing methods. This allows for an unambiguous and efficient description of non-Markovian phenomena, enabling compression and recovery techniques pivotal to near-term technologies. We highlight the implications of our results by analyzing an exactly solvable model to show that memory truncation is possible even in a highly non-Markovian regime.