Daily supervisor: Álvaro G. Iñesta (a.gomezinesta[at]tudelft.nl).

Project supervisor: Stephanie Wehner

* This is a theoretical computer science project, no background in quantum is required *

Quantum networks are expected to enable multi-party applications that are provably impossible by using only classical information. Most of these applications consume shared entanglement as a basic resource. Entanglement distribution protocols are used to generate and share multipartite entanglement among remote parties. Protocols for continuous distribution of entanglement (CD protocols) preemptively distribute entangled states among the nodes, while on-demand (OD) protocols only distribute entanglement after some users request it. We expect CD protocols to provide faster service when the users request entanglement at a very high rate. However, CD protocols are also likely to waste more resources during their operation.

Here, we want to investigate the performance of two simple CD and OD protocols in a dumbbell network. In particular, we want to answer the following research questions:

1. For what values of request submission rate does a CD protocol provide higher entanglement distribution rates than an OD protocol?
2. What is the extra cost associated with running a CD protocol versus an OD protocol?

Figure 1: Illustration of a dumbbell quantum network with six users and three repeaters. Physical channels are represented as solid lines and entanglement as wavy lines. The users in the left side of the dumbbell want to share entanglement with users in the right side. Entanglement requests are submitted by a pair of users.

Goals of the Project:

• Analytically, compute the mean sojourn time (MST) and the load of the system for each protocol.
• Define a cost function (e.g., number of quantum operations per unit time) for the protocols.
• Analytically, compute the cost of each protocol.
• Compare MST, load, and cost of each protocol for different request submission rates.
• Extra goals:
o Simulate the system to validate the theory.
o Compare our conclusions with the heuristics derived in the performance analysis of CD protocols from [1].

Requirements:

Background in Maths, Computer Science, Physics, or related fields. The student must be familiar with basic concepts from probability theory and statistics. Knowledge on queueing theory and performance analysis is appreciated but not required. No background in quantum is required.
The student must have some experience (or must be willing to learn) Python or Matlab.

References:

[1] Iñesta, Á. G., & Wehner, S. (2023). Performance metrics for the continuous distribution of entanglement in multiuser quantum networks. Physical Review A, 108(5), 052615.