General Communication Enhancement via the Quantum Switch

• URL: http://arxiv.org/abs/2407.02726v1
• Date: Wed, 3 Jul 2024 00:47:13 GMT
• Title: General Communication Enhancement via the Quantum Switch
• Authors: Zhen Wu, James Fullwood, Zhihao Ma, Siqi Zhou, Qi Zhao, Giulio Chiribella,
• Abstract summary: We conjecture that $mathcalP_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $tt SWITCH$. We then formulate a communication protocol involving the quantum $tt SWITCH$ which enhances the private capacity of the BB84 channel.
• Score: 15.779145740528417
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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