General Communication Enhancement via the Quantum Switch

TL;DR

This paper investigates how the quantum switch can enhance communication capacities of quantum channels, introduces a new computable quantity, and proves its relevance for Pauli channels and a protocol for BB84 channel enhancement.

Contribution

It defines a new quantity $ ext{P}_n$ for the quantum switch, conjectures its necessity and sufficiency for communication enhancement, and derives capacity formulas for Pauli channels.

Findings

$ ext{P}_n > 0$ is necessary and sufficient for enhancement in Pauli channels

Derived explicit classical capacity formula for quantum switch of Pauli channels

Proposed a protocol that increases private capacity of the BB84 channel

Abstract

Recent studies have shown that quantum information may be effectively transmitted by a finite collection of completely depolarizing channels in a coherent superposition of different orders, via an operation known as the quantum $\tt SWITCH$. Such results are quite remarkable, as completely depolarizing channels taken in isolation and in a definite order can only output white noise. For general channels however, little is known about the potential communication enhancement provided by the quantum $\tt SWITCH$. In this Letter, we define an easily computable quantity $\mathcal{P}_n$ associated with the quantum ${\tt SWITCH}$ of $n$ copies of a fixed channel, and we conjecture that $\mathcal{P}_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $\tt SWITCH$. In support of our conjecture, we derive a simple analytic expression for the classical capacity of the quantum $\tt SWITCH$ of $n$ copies of an arbitrary Pauli channel in terms of the quantity $\mathcal{P}_n$, which we then use to show that our conjecture indeed holds in the space of all Pauli channels. Utilizing such results, we then formulate a communication protocol involving the quantum $\tt SWITCH$ which enhances the private capacity of the BB84 channel.