Communicating a string of zeros and ones quantumly Alice wants to communicate an arbitrary $x \in \{0 ,1\}^n$ to Bob. Alice and Bob communicate
in rounds, in each round Alice (or Bob) applies a unitary transformation on his/her part and
transmits a qubit to the other side, until at the end Bob measures his state and tries to infer
x. The protocol is successful if for every $x \in \{0,1\}^n$ Bob succeeds with probability 1. Let
$n_A / n_B$ be the number of messages sent by Alice / Bob respectively.

Now I want to show that for any successful protocol we must have $n_A \geq  \lceil n/2 \rceil $, and $n_A+n_B \geq n$, and I need to show that the same argument above follows also for p-successful protocols, i.e if there's a p-successful protocol then the ineqaulities above should also follow for this protocol; a p-successful protocol is one in which Bob succeeds with probability p.

Any hints or prefereably bibliography where this or similar problem is disscused?

Thanks.
This paper proves the results you have described:


  Ashwin Nayak and Julia Salzman. Limits on the Ability of Quantum
  States to Convey Classical Messages. Journal of the ACM, 53(1):
  184-206, 2006.