Universal coding for transmission of private information

Abstract

We consider the scenario in which Alice transmits private classical messages to Bob via a classical-quantum channel, part of whose output is intercepted by an eavesdropper, Eve. We prove the existence of a universal coding scheme under which Alice's messages can be inferred correctly by Bob, and yet Eve learns nothing about them. The code is universal in the sense that it does not depend on specific knowledge of the channel. Prior knowledge of the probability distribution on the input alphabet of the channel, and bounds on the corresponding Holevo quantities of the output ensembles at Bob's and Eve's end suffice.Comment: 31 pages, no figures. Published versio

Universal random codes: capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender

“…where the second inequality above is by Jensen's inequality together with concavity of the square-root function. The last inequality is by the estimate in (16). As a consequence of these bounds, we have…”

“…In both cases, suitable random codes already exist in the literature without having been exploited simultaneous transmission yet. In case of universal classical message transmission, independent first results can be found in [9], [22], and [16]. In this work, we exploit the recent and very powerful techniques which where added to the aforementioned results in [34].…”

“…The compound channel model already has been studied in classical Shannon theory since the 1960s. In the domain of quantum Shannon theory, past research activities regarding compound quantum channels where mostly concentrated on point to point quantum channels, leading to determination of the classical capacity [22,9,16,34], and the quantum capacities [11,12] of the compound quantum channel. Regarding compound quantum channels having more than two users, the research was concentrated on private classical message transmission over wiretap channels, i.e.…”

Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

“…In particular a detailed proof of Lemma 9 is provided. Over the years several code constructions for message transmission over compound cq channels have been established (see [12,22,19,25]). The arguments we invoke below for proving Lemma 9 rely heavily on the techniques Mosonyi's work [25].…”

Preface to the Second Edition

“…Smith (2008) later showed that the symmetric-side-channel-assisted private classical capacity is additive. Datta and Hsieh (2010) demonstrated universal private codes for quantum channels.…”