High Capacity Noisy Unruh--DeWitt Quantum Channels with Bosonic Dephasing

Abstract: Unruh--DeWitt (UDW) detectors implemented as UDW quantum gates provide a framework for evaluating quantum Shannon theory properties of qubit-field systems. UDW quantum channels consist of qubits encoding/decoding quantum information onto/off of quantum fields. With the controlled unitary structure of UDW gates, the encoding/decoding process happens on the diagonals of the coherent state density matrix describing the field. However, given the non-orthogonality of coherent states the output of UDW channels consists of unwanted states and unwanted mixing of states that lower the channel capacity. In idealized models, these appear in the off-diagonals and diagonals of the field's density matrix in the coherent state basis. For this reason, we show that UDW quantum channels have an unexpected representation as certain bosonic dephasing channels with dephasing parameters captured by a combination of the coupling, smearing, and switching functions of the UDW detector model. We demonstrate the unexpected consequence that a larger dephasing parameter results in higher channel capacity and helps alleviate unwanted state mixing. We illustrate these properties through two examples: inserting an additional ideal dephasing channel into the quantum channel and inserting cross-talk noise via a third UDW gate. Remarkably, the cross-talk noise channel qualitatively improves a lower bound on the quantum capacity suggesting UDW gates will have unexpected performance improvements if realized in condensed matter experiments.