A linear Stabilizer Entropy acts as a non-stabilizerness monotone with overwhelming probability for mixed states under non-adaptive Clifford channels on flat stabilizer states, with violation probabilities decaying exponentially with system size.
Statistical properties of random matrix product states
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abstract
We study the set of random matrix product states (RMPS) introduced in arXiv:0908.3877 as a tool to explore foundational aspects of quantum statistical mechanics. In the present work, we provide an accurate numerical and analytical investigation of the properties of RMPS. We calculate the average state of the ensemble in the non-homogeneous case, and numerically check the validity of this result. We also suggest using RMPS as a tool to approximate properties of general quantum random states. The numerical simulations presented here support the accuracy and efficiency of this approximation. These results suggest that any generalized canonical state can be approximated with high probability by the reduced density matrix of a random MPS, if the average MPS coincide with the associated microcanonical ensemble.
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Stabilizer entropy is trustworthy for mixed states
A linear Stabilizer Entropy acts as a non-stabilizerness monotone with overwhelming probability for mixed states under non-adaptive Clifford channels on flat stabilizer states, with violation probabilities decaying exponentially with system size.