Layered-Secrecy Coding Sample Clauses

Layered-Secrecy Coding. We define a layered-secrecy code, where a common message is sent to all receivers, at a rate R0, and two confidential messages are sent at rates R1 and R2 Definition 3. A (2nR0 , 2nR1 , 2nR2 , n) layered-secrecy code for the quantum broadcast channel LA→BE E consists of the m0,m ,m1 2 following: three index sets [1 : 2nRj ], for j = 0, 1, 2, corresponding to the common message for all users, the confidential message of User 1 and User 2, and the confidential message for User 1 alone, respectively; an encoding map FAn from the product set [1 : 2nR0 ] × [1 : 2nR1 ] × [1 : 2nR2 ] to the input Xxxxxxx space HAn ; and three decoding POVMs, {ΓBn } for E E n n Bob and {Ξm0,m1 }, {Υm0 } for Eve 1 and Eve 2, respectively. We denote the code by (F, Γ, Ξ, Υ). Bn An En En F L mˆ 0 mˆ 1 mˆ 2 m2 m , m , m m˜ 0 m˜ 1 m1 m2 m˘ 0 Fig. 6. The quantum broadcast channel with layered secrecy. The communication scheme is depicted in Figure 6. The sender Xxxxx has the system An, and the receivers Bob, Eve 1, and Xxx 2 have the systems Bn, En, and En, respectively. Xxxxx chooses a common message m0 ∈ [1 : 2nR0 ] that is intended for all m0,m ,m1 2 users, a layer-1 confidential message m1 ∈ [1 : 2nR1 ] for Bob and Eve 1, and a layer-2 confidential message m2 ∈ [1 : 2nR2 ], all drawn uniformly at random. She encodes the messages by applying the encoding map FAn which results in an input state ρAn = FAn (m0, m1, m2), and transmits the system An over n channel uses of LA→BE E . Hence, the output state is