Optimal one-shot entanglement sharing

TL;DR

This paper investigates the maximum fidelity of entanglement sharing over a single use of a quantum channel, providing methods to find optimal inputs and analyzing how noise affects entanglement in quantum interconnects.

Contribution

It introduces a practical approach to determine maximum entanglement fidelity and optimal inputs for any quantum channel in a one-shot setting, with new insights into noise effects and channel representations.

Findings

Maximum fidelity can be multiplicative across multiple channel uses.

Optimal inputs may not require full entanglement and can change discontinuously with noise.

A noise parametrization for qubit channels with qubit environments is developed, based on no-cloning principles.

Abstract

Sharing entanglement across quantum interconnects is fundamental for quantum information processing. We discuss a practical setting where this interconnect, modeled by a quantum channel, is used once with the aim of sharing high fidelity entanglement. For any channel, we provide methods to easily find both this maximum fidelity and optimal inputs that achieve it. Unlike most metrics for sharing entanglement, this maximum fidelity can be shown to be multiplicative. This ensures a complete understanding in the sense that the maximum fidelity and optimal inputs found in our one-shot setting extend even when the channel is used multiple times, possibly with other channels. Optimal inputs need not be fully entangled. We find the minimum entanglement in these optimal inputs can even vary discontinuously with channel noise. Generally, noise parameters are hard to identify and remain unknown for most channels. However, for all qubit channels with qubit environments, we provide a rigorous noise parametrization which we explain in-terms of no-cloning. This noise parametrization and a channel representation we call the standard Kraus decomposition have pleasing properties that make them both useful more generally.