Optimal one-shot entanglement sharing

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.

Essentially matches published version

References in corpus (8)

• The Quantum Internet
• Quantum Communication With Zero-Capacity Channels
• The structure of degradable quantum channels
• Unbounded number of channel uses are required to see quantum capacity
• Quantum Capacities of Channels with small Environment
• Entanglement-annihilating and entanglement-breaking channels
• Optimal fidelity for a quantum channel may be attained by non-maximally entangled states
• Ultimate entanglement robustness of two-qubit states against general local noises

Cited by in corpus (2)

• Distilled remote entanglement between superconducting qubits across optical channels
• Maximum expectation of observables with restricted purity states