Probabilistic Channel Distillation via Indefinite Causal Order

TL;DR

This paper explores higher-order indefinite causal order in quantum processes, demonstrating their advantage in probabilistic quantum channel distillation over traditional quantum switches, especially for noisy channels.

Contribution

It introduces higher-order quantum switches, showing they outperform conventional switches in distilling qubit Pauli channels and characterizes their asymptotic rates.

Findings

Higher-order switches enable probabilistic distillation of any qubit Pauli channel.

Distillation rate increases with channel noise, contrary to intuition.

No-go theorem for multi-qubit generalizations.

Abstract

The quantum switch has been widely studied as a prototypical example of indefinite causal order in quantum information processing. However, the potential advantages of utilising more general forms of indefinite causal orders remain largely unexplored. We study higher-order switches, which involve concatenated applications of the quantum switch, and we demonstrate that they provide a strict advantage over the conventional quantum switch in the task of quantum channel distillation. Specifically, we show that higher-order quantum switches enable the probabilistic distillation of any qubit Pauli channel into the identity channel with nonzero probability. This capability contrasts with the conventional quantum switch, which allows only a limited set of Pauli channels to be distilled with nonzero probability. We observe that, counterintuitively, the distillation rate generally increases the noisier the channel is. We fully characterise the asymptotic distillation rates of higher-order superswitches for qubit Pauli channels. Finally, we prove a no-go result for multi-qubit generalisations.