How Quantum Teleportation Works
quantum.country
quantum.country
More precisely, let's say Alice has a qubit X in some unknown state, and also Alice and Bob have a pair of qubits A and B in a certain known state with a preexisting mystical link between them. Now Alice can apply a certain quantum gate to X and A, measure them, and send the two classical bits to Bob over ordinary internet. Then Bob can use these bits to choose which quantum gate to apply to B, making it end up in exactly the same state that X started with. The original state of X is "spent" in the process, Alice can't access it anymore. The mystical link between A and B is also "spent", they can't be used the same way again, unless Alice and Bob bring them physically together and reestablish the link. The coolest part is that if X was mystically linked to something else, then Bob's qubit ends up mystically linked to the same thing.
The math details are pretty simple (some reflections and 45-degree rotations in 4-dimensional space) but involve some unusual notation that this comment is too small to explain.
Alice runs the XOR operation (destroying the data and her copy of the pad), send the result to Bob, who runs it against his copy of the pad, producing the original data.
I'm able to understand other physics concepts like relativity, but quantum mechanics seems too entrenched in mathematics at this point in time. I have a very hard time visualizing what is going on.
http://www.smbc-comics.com/comic/the-talk-3?fbclid=IwAR3vAxI...
I don't know if I was just grumpy from the struggles of trying to parse this, but having the author interrupt every other paragraph with a tangent about how I shouldn't feel bad for not understanding this immediately didn't particularly help matters.
Can you expound on this thought a bit? It's not entirely obvious to my why using math, or mathematical concepts, to explain something necessarily invalidates the explanation.
They're natural consequences of the formalization being described and are explained as physical or visual consequences of moving different elements of the diagram around. This is pretty fascinating because the analysis feels informal given how fluent and visual it is, but it can be completely formalized through a logic of graph transformations which let you translate these graphs into algebraic equations.
I haven't finished the book yet, but building from this formalism they begin to demonstrate how this formalism appropriately describes Hilbert spaces (it's an abstract theory to the more concrete model of Hilbert spaces) which then get us very close to standard Quantum formalisms. You can already begin discussing qubits, various standard quantum bases, and basic computational reasoning based on these systems.
It's a really excellent!
Quantum mechanics is not very amenable to learning by analogy. Especially in an example like this where you're following the evolution of a state vector back and forth and the trick is in how that state is manipulated. In some ways that's a plus. You can't oversimplify important details away. I personally thought this was one of the best pieces for teaching a QC subject that I've ever read. It's clear, it flows, and it's as simple as possible and no simpler.
The only people who sort of grok QM are the ones who have 'artificially machine learned' it after years of working with it. Arguably that's also true of the people who grok classical physics.
> Before we verify that the teleportation circuit works, let's briefly discuss one of the most common questions about quantum teleportation: does it enable faster-than-light communication?
> At first, it looks as though it may – after all, Alice is able to transmit her state |\psi\rangle∣ψ⟩ to Bob, even if he's very distant from her. It'd be quite marvelous if it enabled faster-than-light communication, since that in turn would give rise to many incredible phenomena, including the ability to send information backward in time.
> But while it would be marvelous, it is not possible. You can see the trouble if you think closely about the protocol. Remember, for Bob to recover the state |\psi\rangle∣ψ⟩, Alice must send Bob two bits of classical information. The speed of that transmission is limited by the speed of light. Without that classical information, Bob can't guarantee that he recovers |\psi\rangle∣ψ⟩. Instead, what he has is a distribution over four different possible states. And while I won't prove it here, it turns out to be possible to prove that with only that distribution over states, no information is transferred from Alice to Bob. It's a pity, but that's the way the world seems to work.
Specifically,
> Without that classical information, Bob can't guarantee that he recovers |\psi\rangle∣ψ⟩.
and
> it turns out to be possible to prove that with only that distribution over states, no information is transferred from Alice to Bob.
Why is no information encoded in the distribution? Why can't it be statistically gleaned?