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If Alice wants to send one bit of classical information she can use a qbit. Then Bob needs to know which axis to measure to get the information. This needs an extra agreement between Alice and Bob before starting communication. I can figure out why up or down agreement has no importance here since 0 and 1 are just different and need the same level of agreement (two choices available, one for 0 another for 1).

Using qbits, an extra agreement is needed before sending information. A lamp could be on or off without any need for more agreement (which axis in qbit is an extra agreement).

Has this extra contract any importance?

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In your lamp example, additional information is needed between Alice and Bob for them to agree on how to interpret the lamp. If the lamp is on is it a 1 or a zero? They must agree beforehand. – Brandon Enright May 27 '13 at 1:46
Also, you should re-word your question to avoid the use of "contract" as that makes your question rather unclear. I'd reword it for you but I'm concerned about changing the meaning of your question. – Brandon Enright May 27 '13 at 1:47
@BrandonEnright: That contract (on or off for lamp) also needed for up and down. But extra contract is needed for which axis measurement before such contract. – Xaqron May 27 '13 at 11:36
If you're sending bits over radio waves, you need to agree on a frequency, and on AM or FM modulation. Does this mean that radio communication is somehow less useful than shining a lantern out of the steeple of the Old North Church (which still needed an agreement: "one if by land and two if by sea")? – Peter Shor May 27 '13 at 18:16
@PeterShor: My question is edited. I'm new to QM. In terms of metadata (protocol) qbit is more expensive than bit. This fact signals inefficiency is usage and that was the base of my question. – Xaqron May 28 '13 at 6:47

I'll answer in two ways. First of all, what is wrong with them agreeing which axis to measure? As the comments above state, even classical bits (such as a lamp being on or off) require some prior agreement in order to allow interpretation of the signal. You state that a qubit requires extra agreement. But does it really? Suppose they agree to measure along the up/down axis defined by gravity, or the axis that points towards the north star. This is much less agreement than has been done ahead of time in order for cell phones to agree how to interpret the signals that are sent to them, so you could just as well ask how is it that radio waves can convey information if so much prior agreement is needed.

In general, one assumes that the communicating parties can do as much prior work as needed in order to construct their protocol. Otherwise, even if Alice can send Bob a "1", how would he know that is supposed to mean he should pick up a gallon of milk on his way home from work?

The second point is that there are ways for the qubits themselves to convey the information about which axis should be measured. For example, if Alice wanted to send a million bits of information she could first send a thousand qubits that all spin in the same direction. Bob can do tomography on these to deduce the proper axis. Basically, he measures many possible axes to determine which one consistently gives the same measurement result. Having determined the axis using these calibration qubits, he can then decode the data from the rest.

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