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If E.T. phones home, he won't use entagled qubits

I can recall listening to a radio program some 10-15 years ago. The host of the show believed that it would soon be possible to build a faster-than-light communications system using quantum entangled particles, and interviewed several people from a company who were seeking funding to somehow make that happen.

But why not? 

There would be tremendous value in some sort of "quantum phone" of entangled particles that allowed for transferring messages faster than the speed of light. 

Quantum computers are a real thing now. Quantum key distribution could very well revolutionize public key cryptography. Yet if anything, quantum computing is a misnomer because it understates how fundamental quantum mechanics has been on recent technological innovation. Quantum mechanics has been around for a century now and all modern computers rely to some extent on the principles of quantum mechanics to function.

But there will be no quantum phone.

Let's start by explaining how the quantum phone is usually pitched. Forbes magazine has a 2016 article that explains the idea in plain language:

[...] could we use this property — quantum entanglement — to communicate from a distant star system to our own? [...] You could, for example, keep an entangled particle in an indeterminate state, send it aboard a spacecraft bound for the nearest star, and tell it to look for signs of a rocky planet in that star’s habitable zone. If you see one, make a measurement that forces the particle you have to be in the +1 state, and if you don’t see one, make a measurement that forces the particle you have to be in the -1 state.

You have a particle with a binary state being flicked off and on to communicate information. Just like a transistor inside of a conventional computer processor, right? This doesn't sound all that outrageous.

The problem is with this bit: make a measurement that forces the particle you have to be in the +1 state. There is a conceptual mismatch here: you can either make a measurement or you can force a particle into a different state, but you can't do both at the same time. Either you can interfere with the measurement, which breaks the the relationship between that measurement of your entangled particles, or you can not interfere with the measurement, in which case you will not be able to send any meaningful information this way. Whatever specific process you devise to measure the process, that process will be governed by well-known statistical processes that make it impossible to encode information without sending additional information alongside the entangled bits. 

Even if information is transferred between quantum entangled particles at the moment of their measurement - and that information transfer occurs faster than the speed of light - the relevance of this transfer is limited by the extremely strict limit on what kind of information is traveling: whatever statistical distribution governs the particular quantum process being measured.

All of this has been well established for many, many years - the last major break-though in quantum entanglement was arguably John Bell's theorem, which demonstrated Einstein/Polsky/Rosen's hidden variables interpretation of quantum entanglement was wrong. Bell first published that work in 1963. So why was I hearing a pitch for a quantum phone decades after that? Why does one company claim:

When we conquer communication through quantum entanglement, faster-than-light communications will become a real possibility.

The fact remains: a mountain of theoretical and experimental work demonstrates the speed of light is a hard speed limit in the observable universe. An immense amount of knowledge about the universe can be deduced from that simple fact, but these facts are often obscured by being out of sync with our experience of the world. It is much easier to imagine what life might be like without such a barrier in place (awesome)

The truth is, though, that the lightspeed barrier gets us a lot more than it asks of us. Causality, for one. Luminal particles can travel very fast, but they cannot have mass. This means they cannot experience the flow of time. Without time, it is impossible to say that one thing happened before another thing. This means you cannot say that one thing caused another thing. 

Paradoxes are a clue that we have veered off the right logical track. Remain skeptical of any claims that depend on disregarding special relativity. Even if he got hidden variables wrong, Einstein remains a very safe bet in 2021.

Appendix 8-31-2021 String theorist Joseph Polchinski provided some reasons to believe that superluminal communication via quantum entanglement could in fact be possible - provided that the Everett interpretation of quantum mechanics is correct. John Cramer describes the idea:

He [Polchinski]  goes on to describe an "Everett-Wheeler telephone". In standard QM in the Many Worlds scenario in which the wave function does not collapse, a measurement performed in one MW universe can have no effect on a measurement made in another. Polchinski demonstrates that in non-linear QM such measurements "talk" and can be used for transmission of information from one MW branch universe to another. With Polchinski's non-linear quantum telephones you could talk to yourself at an earlier time or to your alter ego in an alternate universe.

Polchinski's idea for a quantum phone depends upon an idea proposed by Nobel laureate Steven Weinberg. Today it is assumed - and has been assumed for the last century - that the Schrodinger equation is linear. Barton Zwiebach described it this way in his Quantum Physics I course at MIT: "We have two solutions. We can add them. We have a single solution. You can scale it by a number." This is a very basic assumption about how, for example, electromagnetic waves interfere with one another to create a new wave. 

Weinberg noticed that in areas of physics other than quantum physics, there are circumstances in which behavior can become non-linear. Weinberg proposed a methodology for testing for non-linearity, and asked why there could not also be circumstances where non-linearity appears in quantum mechanics, also. Polchinski built on Weinberg's work, demonstrating that the prohibition against superluminal communication is removed when linearity is removed. Polchinski went on to develop a specific non-linear modification to the Schrodinger equation that managed to remove the superluminal behavior of other approaches. The result, though, appears to make it possible to send information across quantum multiverses; Polchinski even provided a possible methodology for doing this that he dubbed the Everett-Wheeler phone.

This really seems a pretty strong argument against everything I said before the appendix. WTF?

The Everett-Wheeler quantum phone isn't as sexy as it sounds. Weinberg provided ideas for how to test for non-linearity in quantum physics, and people have looked for non-linearity. So far, evidence of quantum nonlinearity hasn't been found in the experiments. 

Fans of Polchinski reply that the testing needs to be performed at a higher energy level (essentially, using a bigger particle collider). There is always a bigger collider, there is always a higher energy level (see for example Lost in Math by Sabine Hossenfelder). It might be worth it to test for non-linearity at the LHC, I don't know, but if such a test did happen and no evidence of non-linearity was found, the same complaint could conceivably be made: that we aren't looking in the correct range.

But hey, let's make a giant leap and assume that non-linearity does exist. That doesn't solve all the problems. 

What is the absolute smallest possible amount of information that could be considered a communication? You can probably imagine getting an email with a single integer: 1. You'd probably call this a communication, even though it only includes a single bit of information (1). But really, the email includes an additional layer of information that is transmitted implicitly, by virtue of the fact that the bit was an email. An email implies several additional features that include information that is greatly in excess of a single bit: each email has certain fields called headers that must be included in order to be an email at all. These fields are things like "To:" (the recipient address), "From:" (the sender address), the subject line, etc..

The importance of that secondary data is revealed with a simple thought experiment. Imagine if we removed that implicit wrapper of information from the email. Let's say you turn on your computer, and a single integer - 1 - is displayed on your screen for 30 seconds. The computer then proceeds to boot up normally. Would you consider that to be a message? Most people with some idea of how a computer works would be more likely to assume that the integer was some sort of error in the computer (not an error message, though, because error messages at least indicate that they are an error e.g. by saying "ERROR", which requires more than a single bit of information)

Without the tell-tale signs of an email, the single bit of information lacks any of the characteristics of communication. There is more information contained implicitly in an email that is completely blank then there is in the single bit contained on its own.

And a single bit of information is all that can be sent using an Everett-Wheeler quantum phone. This size limit fundamentally makes bi-directional communication impossible. But bi-directionality would be impossible even without a size limit. This is because it is impossible to select a specific multiverse to send a message to. 

In fact, that somewhat under-estimates how weird the situation would be. If we assume that the Everett or Many Worlds interpretation of quantum mechanics is correct, sending a single-bit message using an Everett-Wheeler phone would in fact create the parallel world that receives the "message". Let that sink in for a minute. We are really asking quite a bit of the word phone here. Even with the most robust data plan available using the most extravagant cellphone available, calling a person on the phone typically will not instantaneously create the person on the other end.