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Renato Renner

Publications and source records attributed to Renato Renner.

151 records · Page 9Linked to original sources
arXiv2006

Locking of accessible information and implications for the security of quantum cryptography

The unconditional security of a quantum key distribution protocol is often defined in terms of the accessible information, that is, the maximum mutual information between the distributed key S and the outcome of an optimal measurement on the adversary's (quantum) system. We show that, even if this quantity is small, certain parts of the key S might still be completely insecure when S is used in applications, such as for one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information might increase the accessible information by more than one bit.

quant-ph↗
arXiv2005

On the Power of Quantum Memory

We address the question whether quantum memory is more powerful than classical memory. In particular, we consider a setting where information about a random n-bit string X is stored in r classical or quantum bits, for r<n, i.e., the stored information is bound to be only partial. Later, a randomly chosen binary question F about X is asked, which has to be answered using only the stored information. The maximal probability of correctly guessing the answer F(X) is then compared for the cases where the storage device is classical or quantum mechanical, respectively. We show that, despite the fact that the measurement of quantum bits can depend arbitrarily on the question F to be answered, the quantum advantage is negligible already for small values of the difference n-r. An implication for cryptography is that privacy amplification by application of a compression function mapping n-bit strings to s-bit strings (for some s<n-r), chosen publicly from a two-universal class of hash functions, remains essentially equally secure when the adversary's memory is allowed to be r quantum rather than only r classical bits.

quant-ph↗
arXiv2004

A de Finetti representation for finite symmetric quantum states

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.

quant-ph↗
arXiv2004

Universally composable privacy amplification against quantum adversaries

Privacy amplification is the art of shrinking a partially secret string Z to a highly secret key S. We show that, even if an adversary holds quantum information about the initial string Z, the key S obtained by two-universal hashing is secure, according to a universally composable security definition. Additionally, we give an asymptotically optimal lower bound on the length of the extractable key S in terms of the adversary's (quantum) knowledge about Z. Our result has applications in quantum cryptography. In particular, it implies that many of the known quantum key distribution protocols are universally composable.

quant-ph↗
arXiv2004

A Generic Security Proof for Quantum Key Distribution

Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational effort. However, security proofs of quantum key distribution are not trivial and are usually restricted in their applicability to specific protocols. In contrast, we present a general and conceptually simple proof which can be applied to a number of different protocols. It relies on the fact that a cryptographic procedure called privacy amplification is equally secure when an adversary's memory for data storage is quantum rather than classical.

quant-ph↗
arXiv2002

Towards Characterizing the Non-Locality of Entangled Quantum States

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 (roughly) log(log(n)) bits of information are required.

quant-ph↗