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Operational Markov condition for quantum processes
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We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process, or the experimental falsifiability of a Markovian hypothesis.
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Tensor-network decoders for process tensor descriptions of non-Markovian noise
A tensor-network-based maximum likelihood decoder is constructed for quantum error correction under process-tensor noise, with an MPS approximation demonstrated on the five-qubit and Steane codes.
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