Recurrence Criteria for Reducible Homogeneous Open Quantum Walks
New criteria deciding when a homogeneous Open Quantum Walk (the open-quantum-systems analogue of a Markov chain, driven by finite-dimensional completely-positive 'coin' operators L, B, R) is recurrent under the average-number-of-returns definition, allowing reducible coins. Includes the first recurrence criterion for Lazy OQWs, a full characterization for dimension-2 lazy coins, a general finite-dimensional non-lazy criterion on Z, and — via the open quantum jump chain relating continuous- and discrete-time walks — a recurrence criterion on the grid Z^2.
Recurrence Criteria for Reducible Homogeneous Open Quantum Walks on the Line Newton Loebens1*
Studies the recurrence of Open Quantum Walks (OQWs) — the open-quantum-systems generalization of classical Markov chains, where transition operators L, B, R (a finite-dimensional 'coin' given by comp…