The Classical Capacity of Additive Quantum Queue-Channels

Abstract

We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we model the sequential processing of qubits using a single server queue, and derive expressions for the classical capacity of such a quantum `queue-channel.' Focusing on two important noise models, namely the erasure channel and the depolarizing channel, we obtain explicit single-letter capacity formulas in terms of the stationary waiting time of qubits in the queue. Our capacity proof also implies that a `classical' coding/decoding strategy is optimal, i.e., an encoder which uses only orthogonal product states, and a decoder which measures in a fixed product basis, are sufficient to achieve the classical capacity of both queue-channels. Our proof technique for the converse theorem generalizes readily -- in particular, whenever the underlying quantum noise channel is additive, we can obtain a single-letter upper bound on the classical capacity of the corresponding quantum queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.

This paper will appear in the IEEE Journal of Selected Areas in Information Theory (Special Issue on Quantum Information Science), 2020. It generalizes arXiv:1804.00906 to include arbitrary encodings and measurements

References in corpus (10)

• Quantum Computing in the NISQ era and beyond
• Quantum information processing with superconducting circuits: a review
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• Capacities of Quantum Erasure Channels
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Towards Large-Scale Quantum Networks
• Conditional control of the quantum states of remote atomic memories for quantum networking
• On Shor's channel extension and constrained channels
• On converse bounds for classical communication over quantum channels

Cited by in corpus (4)

• Restoring quantum communication efficiency over high loss optical fibres
• Quantum Optical Communication in the presence of strong attenuation noise
• n-Qubit Operations on Sphere and Queueing Scaling Limits for Programmable Quantum Computer
• Polar Codes for Erasure and Unital Classical-Quantum Markovian Channels