# Number of classical bits to transmit with quantum state

1. Mar 4, 2013

### spookyfw

Hello dear Physicists,

in my quantum communication class we dealt with dense coding recently. There we also discussed the super-dense coding protocol. For the used Bell-states the possible classical bits one could possibly encode with one state were 2.
Following the protocol it is evident, but is there also a direct way of seeing that the maximum is 2? Using Shannon or Neumann? As far as I get up to now, we could only measure how entangled the states are with Neumann...

A more involved side-project that popped up during class was to find how many bits could be communicated with the following state

$\Psi = 0.5 [ \left(|0>_A - |1>_A + \sqrt{2}|2>_A\right)|0>_B - \left(|0>_A + |1>_A + \sqrt{2}|2>_A\right)|1>_B]$

Using the basis $|\pm> = |0> \pm |1>$ for system B I diagonalized the state (although it looks weird):

$\Psi = 1/2\left( |->_B |0>_A - |+>_B|1>_A + \sqrt(2) |->_B |2>_A \right)$

But how to see from there how many classical bits one could possibly transmit. I am really lost. It was one of these statements: It is easy to see that this state can be used for Dense Coding, due to the non-trivial Schmidt coefficients. Well, the matrix to diagonalize would be first of all rectangular....

I think I am throwing everything a bit together...,
hence if anyone knows how to solve these issues I would be grateful if one would post it :).

have a good one,
spookyfw