Classical-Quantum Arbitrarily Varying Wiretap Channel

The arbitrarily varying channel models transmission over a channel with an state that can change over time. We may interpret it as a channel with an evil jammer. The arbitrarily varying channel was first introduced by Blackwell, Breiman, and Thomasian in [8]. The wiretap channel models communication with security. It was first introduced by Wyner in [12]. We may interpret it as a channel with an evil eavesdropper. The arbitrarily varying wiretap channel models transmission with both a jammer and an eavesdropper. Its capacity has been determined by Bjelaković, Boche, and Sommerfeld in [3]. A quantum channel is a channel which can transmit both classical and quantum information. In this paper, we consider the capacity of quantum channels to carry classical information, or equivalently, the capacity of a classical quantum channels. The classical capacity of quantum channels has been determined by Holevo in [9]. A classical-quantum channel with a jammer is called a classical-quantum arbitrarily varying channel, its capacity has been determined by Ahlswede and Blinovsky in [1]. Bjelaković, Boche, Janßen, and Nötzel gave an alternative proof and a proof of the strong converse in [2]. A classical-quantum channel with an eavesdropper is called a classical-quantum wiretap channel, its capacity has been determined by Devetak in [7], and by N. Cai, Winter, and Yeung in [5]. A classical-quantum channel with both a jammer and an eavesdropper is called a classical-quantum wiretap channel, it is defined as a pair of double indexed finite set of density operators {(ρx,t, σx,t) : x ∈ X , t ∈ Θ} with common input alphabet X connecting a sender with two receivers, one legal and one wiretapper, where t is called a state of the channel pair. The legitimate receiver accesses the output of the first channel ρx,t in the pair (ρx,t, σx,t), and the wiretapper observes the output of the second part σx,t in the pair (ρx,t, σx,t),