Witnessing quantum memory in non-Markovian processes

Christina Giarmatzi1,2 and Fabio Costa1

1Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, QLD 4072 Australia
2University of Technology Sydney, Centre for Quantum Software and Information, Ultimo NSW 2007, Australia

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We present a method to detect quantum memory in a non-Markovian process. We call a process Markovian when the environment does not provide a memory that retains correlations across different system-environment interactions. We define two types of non-Markovian processes, depending on the required memory being classical or quantum. We formalise this distinction using the process matrix formalism, through which a process is represented as a multipartite state. Within this formalism, a test for entanglement in a state can be mapped to a test for quantum memory in the corresponding process. This allows us to apply separability criteria and entanglement witnesses to the detection of quantum memory. We demonstrate the method in a simple model where both system and environment are single interacting qubits and map the parameters that lead to quantum memory. As with entanglement witnesses, our method of witnessing quantum memory provides a versatile experimental tool for open quantum systems.

The study of open quantum systems is a vast field within quantum physics that concerns the interaction between some system and its environment. Its great importance lies on the fact that every experimental realization of a quantum process faces the possibility of noise coming from the environment. Although in small quantum devices the noise is assumed to be uncorrelated (Markovian) this assumption fails as the size and complexity increases, and the various system-environment interactions become correlated (non-Markovian). These non-Markovian processes can be simulated only by adding an external memory that carries the correlations across the different interactions. The memory required to reproduce the process can be quantum or classical, and being able to distinguish between the two types of non-Markovian noise would lead to different ways of finding its source or correcting for it. Therefore, it is desirable to have efficient methods to decide whether an environment carries a classical or quantum memory.

In this work, we provide a first rigorous definition of classical memory in a non-Markovian process and we present a method that detects that a process is non-Markovian with quantum memory. We do this by mapping our problem to the well known problem of entanglement. We apply our method to an example of a non-Markovian process and present our results of detecting a quantum memory.

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