arXiv:2206.04262 · IEEE Information Theory Workshop (ITW)

The Classical Capacity of Quantum Jackson Networks with Waiting Time-Dependent Erasures

Jaswanthi Mandalapu, Krishna Jagannathan

Published Nov 1, 2022• 2 citations

Abstract

We study the fundamental limits of classical communication using quantum states that decohere as they traverse through a network of queues. We consider a network of Markovian queues, known as a Jackson network, with a single source or multiple sources and a single destination. Qubits are communicated through this network with inevitable buffering at intermediate nodes. We model each node as a ‘queue-channel,’ wherein as the qubits wait in buffer, they continue to interact with the environment and suffer a waiting time-dependent noise. Focusing on erasures, we first obtain explicit classical capacity expressions for simple topologies such as tandem queue-channel and parallel queue-channel. Using these as building blocks, we characterize the classical capacity of a general quantum Jackson network with waiting time-dependent erasures. Throughout, we study two types of quantum networks, namely, (i) Repeater-assisted and (ii) Repeater-less. We also obtain optimal pumping rates and routing probabilities to maximize capacity in simple topologies. More broadly, our work quantifies the impact of delay-induced decoherence on the fundamental limits of classical communication over quantum networks.

DOI: 10.1109/itw54588.2022.9965792

Related papers

The Classical Capacity of a Quantum Erasure Queue-Channel

Prabha Mandayam, Krishna Jagannathan, Avhishek Chatterjee

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 quantum erasures, we obtain an explicit single-letter capacity formula 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 the quantum erasure queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.

IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)Jul 1, 20196 citations

Unital Qubit Queue-Channels: Classical Capacity and Product Decoding

Vikesh Siddhu, Avhishek Chatterjee, Krishna Jagannathan +2 more

Quantum queue-channels arise naturally in the context of buffering in quantum networks, wherein the noise suffered by the quantum states depends on the time spent waiting in the buffer. Mandayam (2020) derived a simple upper bound on the classical capacity of an additive queue-channel and showed it to be achievable for the erasure and depolarizing channels. In this article, we characterize the classical capacity for the class of unital qubit queue-channels and show that a simple product (nonentangled) decoding strategy is capacity achieving. As an intermediate step, we present a simpler derivation of an explicit capacity-achieving product decoding strategy for any independent identically distributed unital qubit channel, which may be of interest. As an important special case, we also derive the capacity and optimal decoding strategies for a symmetric generalized amplitude damping queue-channel. Our results provide useful insights toward designing practical quantum communication networks and highlight the need to explicitly model the impact of buffering.

arXiv:2110.02800IEEE Transactions on Quantum EngineeringJun 21, 20245 citations

The Classical Capacity of Additive Quantum Queue-Channels

Prabha Mandayam, Krishna Jagannathan, Avhishek Chatterjee

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.

arXiv:1906.01356IEEE Journal on Selected Areas in Information TheoryAug 1, 202016 citations

Qubits through Queues: The Capacity of Channels with Waiting Time Dependent Errors

Avhishek Chatterjee, Krishna Jagannathan, Prabha Mandayam

We consider a setting where qubits are processed sequentially, and derive fundamental limits on the rate at which classical information can be transmitted using quantum states that decohere in time. Specifically, we model the sequential processing of qubits using a single server queue, and derive explicit expressions for the capacity of such a `queue-channel.' We also demonstrate a sweet-spot phenomenon with respect to the arrival rate to the queue, i.e., we show that there exists a value of the arrival rate of the qubits at which the rate of information transmission (in bits/sec) through the queue-channel is maximized. Next, we consider a setting where the average rate of processing qubits is fixed, and show that the capacity of the queue-channel is maximized when the processing time is deterministic. We also discuss design implications of these results on quantum information processing systems.

arXiv:1804.00906Apr 3, 20180 citations

Qubits through Queues: The Capacity of Channels with Waiting Time Dependent Errors

Krishna Jagannathan, Avhishek Chatterjee, Prabha Mandayam

We consider a setting where qubits are processed sequentially, and derive fundamental limits on the rate at which classical information can be transmitted using quantum states that decohere in time. Specifically, we model the sequential processing of qubits using a single server queue, and derive explicit expressions for the capacity of such a `queue-channel.' We also demonstrate a sweet-spot phenomenon with respect to the arrival rate to the queue, i.e., we show that there exists a value of the arrival rate of the qubits at which the rate of information transmission (in bits/sec) through the queue-channel is maximised. Next, we consider a setting where the average rate of processing qubits is fixed, and show that the capacity of the queue-channel is maximised when the processing time is deterministic. We also discuss design implications of these results on quantum information processing systems.

National Conference on CommunicationsFeb 1, 201914 citations

An Erasure Queue-Channel with Feedback: Optimal Transmission Control to Maximize Capacity

K Nithin Varma, Krishna Jagannathan

A queue-channel is a model that captures waiting time-dependent degradation of information bits—a scenario motivated by quantum communications and delay-sensitive streaming. Recent work has characterised the capacity of the erasure queue-channel [1], and other noise models encountered in quantum communications. In this paper, we study an erasure queue-channel with feedback, and ask after the optimal transmission strategy to minimize waiting-induced erasures. Specifically, we assume that instantaneous feedback of queue-length (or of the queue-channel output) is available at the transmitter, which can modulate the rate of Poisson transmissions into the queue-channel. We pose an optimal control problem using HJB-style equations to maximize the information capacity, when the transmitter can choose from a bounded set of transmission rates. We show (under a numerically verifiable condition) that the optimal transmission policy is a single-threshold policy of the bang-bang type. In other words, transmitting at the maximum (minimum) possible rate when the queue is below (above) a threshold, maximizes the information capacity of the erasure queue-channel with feedback.

IEEE Information Theory Workshop (ITW)Apr 23, 20232 citations