Qubits through Queues: The Capacity of Channels with Waiting Time Dependent Errors
01 Feb 2019-pp 1-6
TL;DR: In this article, the authors 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.
Abstract: 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.
Citations
More filters
TL;DR: A cognitive-memory-based policy for memory management is developed and it is shown that this policy can decrease the average queuing delay exponentially with respect to memory size.
Abstract: Queuing delay is an essential topic in the design of quantum networks. This paper introduces a tractable model for analyzing the queuing delay of quantum data, referred to as quantum queuing delay (QQD). The model employs a dynamic programming formalism and accounts for practical aspects such as the finite memory size. Using this model, we develop a cognitive-memory-based policy for memory management and show that this policy can decrease the average queuing delay exponentially with respect to memory size. Such a significant reduction can be traced back to the use of entanglement, a peculiar quantum phenomenon that has no classical counterpart. Numerical results validate the theoretical analysis and demonstrate the near-optimal performance of the developed policy.
22 citations
TL;DR: This work model the sequential processing of qubits using a single server queue, and derive expressions for the classical capacity of such a quantum ‘queue-channel’, and begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.
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.
9 citations
04 Jun 2019
TL;DR: Focusing on quantum erasures, this work obtains an explicit single-letter capacity formula in terms of the stationary waiting time of qubits in the queue, and implies that a ‘classical’ coding/decoding strategy is optimal and is sufficient to achieve the classical capacity of the quantum erasure queue-channel.
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 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.
6 citations
01 Aug 2020
TL;DR: In this article, the authors consider a queue-channel model where a stream of qubits is processed sequentially and derive a single-letter upper bound on the classical capacity of 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.
4 citations
Posted Content•
TL;DR: It is shown that the capacity of the multiple-access system converges to that of a single- user queue-length dependent system, and an upper bound on the convergence rate is obtained, implying that the best and worst server behaviors of single-user queues are preserved in the sparse multiple- access case.
Abstract: We consider transmission of packets over queue-length sensitive unreliable links, where packets are randomly corrupted through a noisy channel whose transition probabilities are modulated by the queue-length. The goal is to characterize the capacity of this channel. We particularly consider multiple-access systems, where transmitters dispatch encoded symbols over a system that is a superposition of continuous-time $GI_k/GI/1$ queues. A server receives and processes symbols in order of arrivals with queue-length dependent noise.
We first determine the capacity of single-user queue-length dependent channels. Further, we characterize the best and worst dispatch processes for $GI/M/1$ queues and the best and worst service processes for $M/GI/1$ queues. Then, the multiple-access channel capacity is obtained using point processes. When the number of transmitters is large and each arrival process is sparse, the superposition of arrivals approaches a Poisson point process. In characterizing the Poisson approximation, we show that the capacity of the multiple-access system converges to that of a single-user $M/GI/1$ queue-length dependent system, and an upper bound on the convergence rate is obtained. This implies that the best and worst server behaviors of single-user $M/GI/1$ queues are preserved in the sparse multiple-access case.
3 citations
References
More filters
Book•
01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Abstract: Part I Fundamental Concepts: 1 Introduction and overview 2 Introduction to quantum mechanics 3 Introduction to computer science Part II Quantum Computation: 4 Quantum circuits 5 The quantum Fourier transform and its application 6 Quantum search algorithms 7 Quantum computers: physical realization Part III Quantum Information: 8 Quantum noise and quantum operations 9 Distance measures for quantum information 10 Quantum error-correction 11 Entropy and information 12 Quantum information theory Appendices References Index
25,929 citations
TL;DR: In this paper, a review highlights the recent progress which has been made towards improved single-photon detector technologies and the impact these developments will have on quantum optics and quantum information science.
Abstract: This review highlights the recent progress which has been made towards improved single-photon detector technologies and the impact these developments will have on quantum optics and quantum information science.
1,575 citations
TL;DR: A formula for the capacity of arbitrary single-user channels without feedback is proved and capacity is shown to equal the supremum, over all input processes, of the input-output inf-information rate defined as the liminf in probability of the normalized information density.
Abstract: A formula for the capacity of arbitrary single-user channels without feedback (not necessarily information stable, stationary, etc.) is proved. Capacity is shown to equal the supremum, over all input processes, of the input-output inf-information rate defined as the liminf in probability of the normalized information density. The key to this result is a new converse approach based on a simple new lower bound on the error probability of m-ary hypothesis tests among equiprobable hypotheses. A necessary and sufficient condition for the validity of the strong converse is given, as well as general expressions for /spl epsiv/-capacity. >
907 citations
TL;DR: The time is ripe for describing some of the recent development of superconducting devices, systems and applications as well as practical applications of QIP, such as computation and simulation in Physics and Chemistry.
Abstract: During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
809 citations