Renato Renner

FOCS Conference 2022 Conference Paper

Generalised entropy accumulation

• Tony Metger
• Omar Fawzi
• David Sutter
• Renato Renner

The min-entropy of a quantum system A conditioned on another quantum system E describes how much randomness can be extracted from A with respect to an adversary in possession of E. This quantity plays a crucial role in quantum cryptography: the security proofs of many quantum cryptographic protocols reduce to showing a lower bound on such a min-entropy. Here, we develop a new tool, called generalised entropy accumulation, for computing such bounds. Concretely, we consider a sequential process in which each step outputs a system A i and updates a side information register E. We prove that if this process satisfies a natural “non-signalling” condition between past outputs and future side information, the min-entropy of the outputs $A_{1}, \ldots, \ A_{n}$ conditioned on the side information E at the end of the process can be bounded from below by a sum of von Neumann entropies associated with the individual steps. This is a generalisation of the entropy accumulation theorem (EAT) [1], which deals with a more restrictive model of side information: there, past side information cannot be updated in subsequent rounds, and newly generated side information has to satisfy a Markov condition. Due to its more general model of side-information, our generalised EAT can be applied more easily and to a broader range of cryptographic protocols. In particular, it is the first general tool that is applicable to mistrustful device-independent cryptography. To demonstrate this, we give the first security proof for blind randomness expansion [2] against general adversaries. Furthermore, our generalised EAT can be used to give improved security proofs for quantum key distribution [3], and also has applications beyond quantum cryptography.

TCS Journal 2018 Journal Article

Toward an algebraic theory of systems

• Christian Matt
• Ueli Maurer
• Christopher Portmann
• Renato Renner
• Björn Tackmann

We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is irrelevant, a generalized form of associativity. Composition-order invariance explicitly captures a common property that is implicit in any context where one can draw a figure (hiding the drawing order) of several connected systems, which appears in many scientific contexts. This abstract algebra captures settings where one is interested in the behavior of a composed system in an environment and wants to abstract away anything internal not relevant for the behavior. This may include physical systems, electronic circuits, or interacting distributed systems. One specific such setting, of special interest in computer science, are functional system algebras, which capture, in the most general sense, any type of system that takes inputs and produces outputs depending on the inputs, and where the output of a system can be the input to another system. The behavior of such a system is uniquely determined by the function mapping inputs to outputs. We consider several instantiations of this very general concept. In particular, we show that Kahn networks form a functional system algebra and prove their composition-order invariance. Moreover, we define a functional system algebra of causal systems, characterized by the property that inputs can only influence future outputs, where an abstract partial order relation captures the notion of “later”. This system algebra is also shown to be composition-order invariant and appropriate instantiations thereof allow to model and analyze systems that depend on time.

TCS Journal 2014 Journal Article

Preface

• Tal Mor
• Renato Renner

TCS Journal 2013 Journal Article

The impossibility of non-signaling privacy amplification

• Esther Hänggi
• Renato Renner
• Stefan Wolf

Barrett, Hardy, and Kent have shown in 2005 that protocols for quantum key agreement exist, the security of which can be proven under the assumption that quantum or relativity theory is correct. More precisely, this is based on the non-local behavior of certain quantum systems, combined with the non-signaling postulate from relativity. An advantage is that the resulting security is independent of what (quantum) systems the legitimate parties’ devices operate on: they do not have to be trusted. Unfortunately, the protocol proposed by Barrett et al. cannot tolerate any errors caused by noise in the quantum channel. Furthermore, even in the error-free case it is inefficient: its communication complexity is Θ ( 1 / ε ) when forcing the attacker’s information below ε, even if only a single key bit is generated. Potentially, the problem can be solved by privacy amplification of relativistic — or non-signaling — secrecy. We show, however, that such privacy amplification is impossible with respect to the most important form of non-local behavior, and application of arbitrary hash functions.

TCS Journal 2013 Journal Article

Towards characterizing the non-locality of entangled quantum states

• Renato Renner
• Stefan Wolf

The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for n players demonstrating this non-local property of quantum mechanics: While, on the one hand, it is immediately clear that classical players will lose the game with substantial probability, it can, on the other hand, always be won by players sharing an entangled quantum state. The simplicity of the classical analysis of our game contrasts the often quite involved analysis of previously proposed examples of this type. In the second part, aiming at a quantitative characterization of the non-locality of n -partite quantum states, we consider a general class of n -player games, where the amount of communication between certain (randomly chosen) groups of players is measured. Comparing the classical communication needed for both classical players and quantum players (initially sharing a given quantum state) to win such a game, a new type of separation results is obtained. In particular, we show that in order to simulate two separated qubits of an n -partite GHZ state at least Ω ( log log n ) bits of information are required.