[reeboo]

"You see, Einstein had a problem with it because it seems to conflict with the speed of light limit in Special Relativity. We know today that this is not the case, quantum mechanics does not conflict with Special Relativity because no useful information can be sent between entangled particles." -- So how does quantum communication work? I thought it leveraged entanglement to convey information such that it became untamperable.

[roywiggins]

Quantum entanglement can't be used to send information without also sending some photons or other signal between two locations. That's one problem Einstein had with entanglement- at the time, it looked like entanglement might let you send information "at a distance" without transmitting anything. It turns out that entanglement is real but it conspires to prevent any entangled correlations from actually conveying classical information on their own.[0]

The idea behind quantum cryptography is to send photons from A to B that are specially prepared so that any attempt to read those photons in flight would be detected. You use these photons to pick a shared key, and then communicate between A and B using that key via a classical channel. If you detect someone snooping on the initial key exchange, you can toss that key and try again.

[0] https://en.wikipedia.org/wiki/No-communication_theorem

[btouellette]

Quantum communication isn't communication in the sense that you can decide what to send. You have a shared quantum state due to entanglement and you can guarantee that both sides see the same information when they observe the state but it's more like putting two identical messages into sealed envelopes and sending them off to be opened later (with the caveat that because the message hasn't been determined until it is observed you can prevent anyone from knowing what it is ahead of time).

Much more detailed explanation here: https://www.forbes.com/sites/chadorzel/2016/05/04/the-real-r...

[attilakun]

But you _can_ decide what to send! It's just that the sending is never faster than the speed of light because it always involves the transportation of some physical stuff. In the case of superdense coding, you have to send one half of an entangled particle-pair which can't be done faster than the speed of light. The benefit is that you can send 2 bits of classical information by transporting only one (entangled) qubit.

In case of quantum teleportation, you need to send two bits of classical information via whatever mechanism you want to use which again can't be done faster than the speed of light. The benefit is that you can transport the quantum-state of the sender's qubit.

[evanb]

In superdense coding you send one quantum bit ahead of time and hang onto it’s entangled partner. Then later you send one classical but which, when combined with the quantum bit you shared earlier, conveys two classical bits of your choice.

[attilakun]

You don't send any classical bits in superdense coding. You start out with a pair of entangled qubits in the state |00>+|11>. Then, if Alice has the first qubit and Bob has the second, by manipulating the first qubit Alice can perform 4 actions:

1. Nothing, which leaves the combined state unchanged: |00>+|11>.

2. Flip the sign of the base state |11>, thereby changing the combined state to |00>-|11>.

3. Flip the first bit which changes the combined state to |10>+|01>.

4. Perform choice 3 and flip the sign of base state |10>, which changes the combined state to -|10>+|01>.

Now notice that all 4 possible combined states are orthogonal to each other. But we reached each orthogonal state by manipulating only Alice's qubit. When Bob receives Alice's qubit he can put the 2 qubits together and see which state the combined system is in. You wouldn't be able to do this by sending a classical bit as that can't participate in entanglement. And entanglement is needed to access 4 different orthogonal states via manipulating just one qubit.

[evanb]

You're right---I forgot the protocol. Thanks for the correction!

[modzu]

Note it is only a theorem. From the wiki:

"The theorem is built on the basic presumption that the laws of quantum mechanics hold."

They may not.

[Strilanc]

Theorems are the highest standard of proof we have, so it's a bit strange to describe a result as "only a theorem".

But yes, the theorem does assume the postulates of quantum mechanics as preconditions. It's not possible to make any statement about reality that doesn't have this kind of "if it works this way" postulate.

[modzu]

yes, i regret using "only"; i meant "only" that theorems are still subject to experimental verification and also a single theorem can support multiple interpretations.

[vecter]

This isn't a very fair assessment. All evidence we've gathered so far seems to indicate that they do. Of course you're technically right to say that "they may not", but that's true of any physical theory, so it's not particularly meaningful.