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2

Bob can't know in any sense that Alice has sent a message, until and unless Bob receives a classical message from Alice confirming that she has sent a qubit. Even for the sake of argument, let's suppose he somehow knew that Alice has sent a qubit, then arises two scenarios - one, Bob knew it instantly and second, Bob knows only after the time it takes for a ...

5

If you are talking about the idea that the quantum state is encoded on a physical system (perhaps an atom), and that system can be sent from Alice to Bob, then yes, you can detect the presence of the atom without measuring the state of the atom. To make the point, I'm going to go a bit crazy. I'm not claiming this is exactly a physical scenario.... Imagine ...

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There are lots of different situations one can talk about from a cryptography perspective. But here's one that has a huge practical relevance: There are physical realisations of quantum computers which, individually, are limited in the number of qubits they can use. For example, ion traps. For the sake of argument, assume you can hold 10 qubits in each ion ...

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There are two different complexity considerations that you might be interested in in this scenario. The one that most people think about is the communication complexity, i.e. how many qubits Alice and Bob have to send to the referee. This is relatively simple to calculate - it's just $mk$ where $k$ is the number of times you have to repeat the controlled-...

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