Entanglement generation with a quantum channel and a shared state

TL;DR

This paper introduces the channel-state coding protocol in quantum Shannon theory, enabling entanglement generation using noisy channels and shared states, with implications for quantum error correction and superactivation.

Contribution

It presents a new protocol that unifies and extends previous entanglement generation methods, and demonstrates superactivation with zero-capacity channels and bound entangled states.

Findings

Derives the mother and father protocols as special cases.

Formulates entanglement-assisted quantum error-correcting codes.

Demonstrates superactivation with a zero-capacity erasure channel.

Abstract

We introduce a new protocol, the channel-state coding protocol, to quantum Shannon theory. This protocol generates entanglement between a sender and receiver by coding for a noisy quantum channel with the aid of a noisy shared state. The mother and father protocols arise as special cases of the channel-state coding protocol, where the channel is noiseless or the state is a noiseless maximally entangled state, respectively. The channel-state coding protocol paves the way for formulating entanglement-assisted quantum error-correcting codes that are robust to noise in shared entanglement. Finally, the channel-state coding protocol leads to a Smith-Yard superactivation, where we can generate entanglement using a zero-capacity erasure channel and a non-distillable bound entangled state.