Quantum privacy and quantum wiretap channels

Following Schumacher and Westmoreland, we address the problem of the capacity of a quantum wiretap channel. We first argue that, in the definition of the so-called 'quantum privacy,' Holevo quantities should be used instead of classical mutual information. The argument actually shows that the security condition in the definition of a code should limit the wiretapper's Holevo quantity. Then we show that this modified quantum privacy is the optimum achievable rate of secure transmission.