For unitaries from local or pairwise interactions, depolarizing noise above a critical strength makes open quantum spin chain dynamics exactly classically simulable by halting growth in the negative Markov chain representation.
The conservation of probability for the matrix Mtranslates into ⃗1T M= 0, which is equivalent to L∗P C PC = 0
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Quantum-to-Classical Computability Transition via Negative Markov Chains
For unitaries from local or pairwise interactions, depolarizing noise above a critical strength makes open quantum spin chain dynamics exactly classically simulable by halting growth in the negative Markov chain representation.