Semantic Security for Quantum Wiretap Channels Holger Boche Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, Munich Center for Quantum Science and Technology (MCQST) Munich, Germany
[email protected] Minglai Cai Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, Munich, Germany
[email protected] Christian Deppe Lehr- und Forschungseinheit für Nachrichtentechnik Technische Universität München, Munich, Germany
[email protected] Roberto Ferrara Lehr- und Forschungseinheit für Nachrichtentechnik Technische Universität München, Munich, Germany
[email protected] Moritz Wiese Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, Munich Center for Quantum Science and Technology (MCQST) Munich, Germany arXiv:2001.05719v1 [quant-ph] 16 Jan 2020
[email protected] January 17, 2020 Abstract We determine the semantic security capacity for quantum wiretap channels. We extend methods for classical channels to quantum chan- nels to demonstrate that a strongly secure code guarantees a semantically secure code with the same secrecy rate. Furthermore, we show how to 1 transform a non-secure code into a semantically secure code by means of biregular irreducible functions (BRI functions). We analyze semantic security for classical quantum channels and for quantum channels. Contents 1 Introduction 2 2 Basic Notations and Definitions 4 3 Strong and Semantic security 7 3.1 Codes ................................. 7 3.2 Capacities............................... 9 3.3 Derandomization ........................... 11 3.4 QuantumChannels.......................... 13 4 Semantic Secrecy Capacity 15 5 Semantic Security with BRI Functions 20 5.1 BRIfunctions............................. 20 5.2 BRImodularcodes.......................... 29 6 Further Perspectives 32 A Technical Lemmas 36 1 Introduction We investigate the transmission of messages from a sending to a receiving party through a wiretap channel.