Sharing entanglement efficiently

Abstract

Quantum networks are expected to enable applications that are provably impossible with classical communication alone, such as generation of secret keys for secure communication and high-precision distributed sensing. A fundamental resource needed for many of these applications is shared entanglement among distant parties. Hence, the viability of an application relies on the underlying protocol for entanglement distribution. Existing protocols often suffer from long waiting times, as they rely on the success of multiple random events, each with a low probability of success. Moreover, pre-distribution of entanglement is difficult, since entanglement degrades over time when stored in memory, eventually becoming unusable. In this thesis, we address these challenges by designing efficient entanglement distribution protocols and architectures.

First, we focus on on-demand entanglement distribution, in which the entanglement distribution process is initiated only after some users request it. We find optimal protocols that minimize the waiting time for distributing entanglement among two users that are connected by a chain of two-way quantum repeaters. The performance of these protocols sets a benchmark for on-demand distribution of quantum states. We also study a multi-user network of one-way quantum repeaters, and we conclude that finite waiting times are only achievable when the users are at most a few kilometers apart from each other, irrespective of the number of repeaters available.

Next, we examine protocols for continuous entanglement distribution, in which the distribution process is initiated before any user requests. While these protocols can sometimes lead to resource wastage – as noise in memory renders the entanglement
unusable if distributed too early –, they offer the potential to reduce expected waiting times compared to on-demand methods. Surprisingly, we find that, when the time required to distribute entanglement follows a broad probability distribution, initiating the process preemptively can actually result in longer expected waiting times compared to an on-demand approach.

Lastly, we propose an architecture for buffering high-quality entanglement, ensuring it is readily available for use when needed. A key feature of this system is the use of purification subroutines to prevent the buffered entanglement from degrading over time due to quantum decoherence. Among other findings, we show that maximizing entanglement quality upon consumption requires frequent purification, even if this process often fails and results in the loss of high-quality buffered entanglement. The results presented in this dissertation were obtained mostly analytically, leveraging tools from performance analysis, including queueing theory and renewal theory, and supported by extensive discrete-event simulations. Our theoretical insights provide benchmarks and identify fundamental limitations of quantum networks, offering valuable guidance for the design of reliable entanglement distribution systems.