Full characterisation of quantum non-Markovian processes: from tomography to noise detection.*

Every experimental realisation 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 increase, and the various system-environment interactions become correlated (non-Markovian).

We present a method of full quantum process tomography that captures non-Markovian noise and a method to detect quantum memory in a non-Markovian process [1]. 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 the state can be mapped to a test for quantum memory in the process.

We demonstrate the method in a simple toy model, but our methods have been applied experimentally, too, in photonics [2] and superconducting qubits [3].

[1] C. Giarmatzi and F. Costa Quantum 5, 440 (2021)

[2] K. Goswami, C. Giarmatzi, et al. Phys. Rev. A 104, 022432 (2021)

[3] Upcoming paper