Incomplete pure dephasing of N-qubit entangled W states

TL;DR

This paper investigates how spatial separation affects the decoherence of entangled N-qubit W states in a bosonic heat bath, revealing conditions under which decoherence can be suppressed or mitigated.

Contribution

It introduces a causal master equation that accurately describes non-Markovian decoherence dynamics considering qubit separation, improving upon standard models.

Findings

Spatial noise correlations can prevent complete dephasing.

The causal master equation captures non-Markovian effects missed by Bloch-Redfield.

Decoherence-poor subspaces are identified for quantum error correction.

Abstract

We consider qubits in a linear arrangement coupled to a bosonic field which acts as a quantum heat bath and causes decoherence. By taking the spatial separation of the qubits explicitly into account, the reduced qubit dynamics acquires an additional non-Markovian element. We investigate the time evolution of an entangled many-qubit W state, which for vanishing qubit separation remains robust under pure dephasing. For finite separation, by contrast, the dynamics is no longer decoherence-free. On the other hand, spatial noise correlations may prevent a complete dephasing. While a standard Bloch-Redfield master equation fails to describe this behavior even qualitatively, we propose instead a widely applicable causal master equation. Here we employ it to identify and characterize decoherence-poor subspaces. Consequences for quantum error correction are discussed.