Okay, folks, I'm gonna have to do a long thread on #QuantumInternet. Keep your eyes peeled...
Said in my best Marvin the Martian voice: Delays, delays!
#QuantumInternet thread coming up. This was posted first on the bird site to contact the creator of the video that prompted it, so some of it is written second person to her.
Hi Sabine, let's talk #QuantumInternet. We did this a few years ago, when I generated a tweetstorm about #QuantumComputerArchitecture, and I had been thinking it was about time to do something similar for quantum communications and Quantum Internet.
(For those with short memories, see https://twitter.com/rdviii/status/1291629048288878593 for tweets or a PDF of the whole thing.)
Rod Van Meter 🌻 (@rdviii) on X

Better yet, link to the actual document. Interested in #QuantumComputerArchitecture? Check this out. https://t.co/ID5WB4h0pA

X (formerly Twitter)
Your video on #QuantumInternet brings up some interesting points, which I want to explore in a little more depth than you went into.
Let's talk about potential uses for a network that distributes entanglement, then about the distinction of different types of networks, then I want to expand on your cookie analogy. We'll end with some references. (I'll toss a few in here and there in the thread, too.)
It's not going to be as long and as technical as that #QuantumComputerArchitecture thread, though.
You described the #QuantumInternet as "a solution in search of a problem", and while that's rather glib, it's not completely unjustified. The shift analog-->digital-->quantum information is so deep and profound, we will be exploring it for decades.
For quite some years, most of us in the field (including me) have been dividing use cases for quantum networks into three categories: cryptographic functions, sensor networks, and distributed quantum computing.
For one summary of these three categories aimed at advancing work on #QuantumInternet within the Internet engineering community (#IETF and #IRTF), see
https://datatracker.ietf.org/doc/draft-irtf-qirg-quantum-internet-use-cases/
Application Scenarios for the Quantum Internet

The Quantum Internet has the potential to improve application functionality by incorporating quantum information technology into the infrastructure of the overall Internet. This document provides an overview of some applications expected to be used on the Quantum Internet and categorizes them. Some general requirements for the Quantum Internet are also discussed. The intent of this document is to describe a framework for applications, and describe a few selected application scenarios for the Quantum Internet.This document is a product of the Quantum Internet Research Group (QIRG).

IETF Datatracker
Information on RFC 9340 » RFC Editor

The only one you discussed in your video is quantum key distribution (QKD), the canonical example of a quantum crypto function. It would replace the classical Diffie-Hellman key exchange portion of an encrypted classical communication session.
(An encrypted conversation consists of, roughly, three phases: authentication, key generation, and encryption of the message, or bulk data encryption.)
QKD is a surprising and important concept, but just replacing D-H is unlikely to be sufficient incentive to build an entire new communication infrastructure. The other crypto functions, such as leader election, would fall into that same category.
So what about the other two? First we need to know about the difference between entangled and unentangled quantum networks. QKD can run either with or without entanglement.
Networks that provide quantum entanglement as a service are much, much broader in potential applications, but are much, much harder to build.
I'm lumping several different things together in the category of sensor networks. Examples include high-precision clock synchronization, improved resolution in arrays of telescopes, and the like.
These are great theoretical ideas, but are incredibly challenging to implement and require VERY high rates of entanglement generation.
(Entanglement is a consumable; once you have used it once, it's gone, so "data rates" for making new entanglement are critical.)
While it's not the same thing as the entangled #QuantumInternet, one use of related technology is in production in LIGO, the gravitational wave observatory, which uses squeezed light:
https://www.ligo.caltech.edu/news/ligo20231023
LIGO Surpasses the Quantum Limit

New technology in operation at LIGO is tackling quantum mechanical noise, enabling LIGO to probe a larger volume of the Universe and greatly boost the observatory's ability to study the exotic events that shake space and time.

LIGO Lab | Caltech
So the sensor networks are attractive but difficult, especially when doing the engineering of the classical interface and control and worrying about noise.
Which brings us to distributed #QuantumComputing.
Which in turn requires us to talk about types of network deployments, which don't get enough attention, IMO, though that's improving a little.