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 ๐ŸŒป (@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 ยป 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.
Especially, we need to understand that there are similarities and differences between system interconnects or data center networks and wide-area networks.
https://www.osti.gov/biblio/1900586
A Roadmap for Quantum Interconnects (Technical Report) | OSTI.GOV

The U.S. Department of Energy's Office of Scientific and Technical Information

It's critical to know that *scaling up quantum computers requires entanglement between quantum processors*. If we want to use two small quantum computers to solve one larger problem, we MUST be able to create inter-node entanglement.
A network of small nodes coupled via an entangling interconnect is what I call a quantum multicomputer. We talked about designs like this in the #QuantumComputerArchitecture tweetstorm.
https://zenodo.org/records/3496597
A #QuantumComputerArchitecture Tweetstorm

A record of a 186-tweet description of the field of quantum computer architecture. This is essentially an annotated bibliography of over 100 journal and conference papers.

Zenodo
It's a MUST, a GOTTA HAVE, a NOT OPTIONAL technology. It's by far the clearest argument in favor of a quantum network.
No entanglement, no scalability.
Beyond that, what about wide-area entangling networks? One of my favorite ideas of the last two decades is blind quantum computation, by Broadbent, Kashefi and Fitzsimons.
https://arxiv.org/abs/0807.4154
Universal blind quantum computation

We present a protocol which allows a client to have a server carry out a quantum computation for her such that the client's inputs, outputs and computation remain perfectly private, and where she does not require any quantum computational power or memory. The client only needs to be able to prepare single qubits randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Our protocol is interactive: after the initial preparation of quantum states, the client and server use two-way classical communication which enables the client to drive the computation, giving single-qubit measurement instructions to the server, depending on previous measurement outcomes. Our protocol works for inputs and outputs that are either classical or quantum. We give an authentication protocol that allows the client to detect an interfering server; our scheme can also be made fault-tolerant. We also generalize our result to the setting of a purely classical client who communicates classically with two non-communicating entangled servers, in order to perform a blind quantum computation. By incorporating the authentication protocol, we show that any problem in BQP has an entangled two-prover interactive proof with a purely classical verifier. Our protocol is the first universal scheme which detects a cheating server, as well as the first protocol which does not require any quantum computation whatsoever on the client's side. The novelty of our approach is in using the unique features of measurement-based quantum computing which allows us to clearly distinguish between the quantum and classical aspects of a quantum computation.

arXiv.org
Maybe the most intriguing thing I have seen in recent years is the combination of quantum computing and quantum sensing, from the group surrounding John Preskill at Caltech, especially the astounding Robert Huang.
https://scholar.google.com/citations?user=2y5YF-gAAAAJ&hl=en
Hsin-Yuan Huang (Robert)

California Institute of Technology, Google Quantum AI - Cited by 4.971 - Quantum Information - Machine Learning - Quantum Many-Body Physics

They have shown how coupling a quantum sensor to a quantum computer *dramatically* reduces the number of times you need to actually run the quantum experiment.
https://arxiv.org/abs/2112.00778
Quantum advantage in learning from experiments

Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.

arXiv.org
This is one of the most important ideas in recent years, IMO, and it will take us years to figure out all of its implications. It might be used in either a lab+data center configuration, or wide-area setup, it's not clear yet.
All of this work is supported on what, by my estimate, is about 1% of what's being spent on #QuantumComputing. It's a small but critical part of an entire ecosystem.
Okay, I think that covers what I wanted to say about the utility of entangled networks, both data center and wide-area. Let me also comment on the cookie:
The cookie analogy for entanglement is incomplete, and simplified to the point where it's misleading. Let me see if I can do a little better, but this makes it a LOT longer and murkier, so stick with me...
A cookie has two properties, perhaps flavor (chocolate and vanilla) and shape (round and square), but when you are given a cookie you can't learn about both. You have to pick one.
You can either feel the shape with your hand or you can taste it, but not both, and if you try to look at it instead it just crumbles before you can learn anything about it.
The Quantum Internet is a Magic Cookie Pair Machine. Its job is to make special pairs of cookies and give one to me and one to you.
These pairs of cookies are correlated in a weird way.
You and I ask the Quantum Internet to make a special pair for us. Then we each, independently, decide whether to taste our cookie or feel it, then we share what we found.
Strangely, if we both tasted it, we got the SAME flavor. If we both felt it, we found the SAME shape.
But if one of us tasted it and one of us felt it, each of us just gets a random result.
Of course, if we do this just once, it doesn't tell us much. In fact, we have to repeat this a bunch of times, and what we get is just this weird statistical result.
Until the advent of quantum computing, that's all this was, a weird statistical anomaly, with the profound but esoteric suggestion that quantum mechanics and relativity don't mix.
Nowadays it's critical to the operation of a quantum computer on the inside, but the question at hand is whether it is useful over longer distances. I hope the discussion above gives you some idea of the things we are working to realize.
If you're with me so far, that's roughly the way we use entanglement; taking some combination of the shape and flavor and mixing it with the other qubits at each end to entangle larger sets of qubits. But there's actually a catch in entanglement:
If we just talk about the flavor or shape, well, the cookies might have secretly been shaped & flavored, but we just don't what they are. That would just be classical correlation, not entanglement.
If, instead, we do something odd and measure, well, let's call it flape, not quite flavor or shape. We might find choquare or vacircle.
THEN it turns out that there is still a statistical correlation between the outcomes of the measurements (shape, flavor, flape) at the two ends...in some way that CANNOT be just a hidden characteristic of the already-shared cookies.
@rdviii This gave me flashbacks to philosophy tutorials on Hume's puzzle of the colour "grue"! ๐Ÿ’š๐Ÿ’™