Now is a good moment to introduce Alice and Bob (not their real names): our two protagonists who always need to communicate with each other, in scenarios of varying complexity and danger. These two play the major role in many communication dramas, though they remain rather lacking in character development. In this episode of their story, Alice is sending quantum states, called carriers, to Bob, and Bob is trying his best to correctly identify them by choosing appropriate measurements.
Let us start with a simple observation: if the carriers are described by state vectors in a
But can Alice and Bob do better than that?
Can Alice send more than
The answer is no.
This is just like the classical scenario: the space of binary strings of length
n(which encode exactly nbits of information, by definition) is of dimension 2^n, since we describe any such string by picking between 0and 1for each digit, and we have n-many digits.↩︎