Renato Renner

In Wigner's friend-type experiments, unlike in standard QIP setups, the participating agents are modelled as quantum systems. Recent versions of such experiments have revealed that the usual rules for combining information held by different agents are inconsistent with quantum theory. Here, we show that this insight is relevant to paradoxes in quantum gravity, such as the black hole firewall paradox. This is because their structure is similar to Wigner's friend experiments: they rely on combining knowledge of multiple agents, some of whom enter the black hole, which is treated as a quantum system.

Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the accuracy achievable with a given amount of nonequilibrium resources. The limit applies to arbitrary information processing tasks and arbitrary information processing systems subject to the laws of quantum mechanics. It is easily computable and is expressed in terms of an entropic quantity, which we name the reverse entropy, associated to a time reversal of the information processing task under consideration. The limit is achievable for all deterministic classical computations and for all their quantum extensions. As an application, we establish the optimal tradeoff between nonequilibrium and accuracy for the fundamental tasks of storing, transmitting, cloning, and erasing information. Our results set a target for the design of new devices approaching the ultimate efficiency limit, and provide a framework for demonstrating thermodynamical advantages of quantum devices over their classical counterparts. This also implies a thermodynamic benchmark to certify genuine quantum devices from their classical simulation.

The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on techniques such as noisy preprocessing and random key measurements. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of 9.26%, exceeding all previously known noise thresholds. Furthermore, we also consider in greater detail a particular form of generalized CHSH inequality, and derive partial closed-form results for such cases. We discuss the potential advantage of this approach for realistic photonic implementations of DIQKD.

Abstract A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum processor can exist, approximate processors have been proposed in the past two decades. A fundamental open question is how the size of the smallest quantum program scales with the approximation error. Here we answer the question, by proving a bound on the size of the program and designing a concrete protocol that attains the bound in the asymptotic limit. Our result is based on a connection between optimal programming and the Heisenberg limit of quantum metrology, and establishes an asymptotic equivalence between the tasks of programming, learning, and estimating unitary gates.

Quantum Key Distribution (QKD), invented by Bennett and Brassard and Ekert can be considered the first application of quantum information science. We focus on the assumption that an arbitrarily large number M of signals can be exchanged between the legitimate parties (Alice and Bob) and subsequently used for the computation of the final key. Here, we apply a novel proof technique to the BB84 QKD protocol and derive almost tight bounds on the minimum value M required to achieve a given level of security. The technique is based on a formulation of the uncertainty relation in terms of smooth entropies. We demonstrate significant improvements of the finite-key rate over existing results.

We reverse-engineer, test and analyse hardware and firmware of the commercial quantum-optical random number generator Quantis from ID Quantique. We show that > 99% of its output data originates in physically random processes: random timing of photon absorption in a semiconductor material, and random growth of avalanche owing to impact ionisation. We have also found minor non-random contributions from imperfections in detector electronics and an internal processing algorithm. Our work shows that the design quality of a commercial quantum-optical randomness source can be verified without cooperation of the manufacturer and without access to the engineering documentation.

Device-independent quantum key distribution provides security even when the equipment used to communicate over the quantum channel is largely uncharacterized. An experimental demonstration of device-independent quantum key distribution is however challenging. A central obstacle in photonic implementations is that the global detection efficiency, i.e., the probability that the signals sent over the quantum channel are successfully received, must be above a certain threshold. We here propose a method to significantly relax this threshold, while maintaining provable device-independent security. This is achieved with a protocol that adds artificial noise, which cannot be known or controlled by an adversary, to the initial measurement data (the raw key). Focusing on a realistic photonic setup using a source based on spontaneous parametric down conversion, we give explicit bounds on the minimal required global detection efficiency.

In security applications, it is necessary to use random numbers with the highest possible entropy. Quantum Random Number Generators (QRNG) are most suitable for creating such numbers due to the non-deterministic nature of quantum physics. In this work we present the different steps of the construction of a new design for a high-speed QRNG. Furthermore, in order to make our QRNG suitable for use in security applications, we explain the steps we are taking to make it conform to security standards. Such standards exist and define guidelines for the design of classical Random Number Generators. However, for QRNG, it is necessary to make adaptations, which requires additional work in its design, realization and evaluation with respect to security standards.

Although the secrecy condition for quantum key distribution (QKD) introduced by Renner is broadly accepted, it does not conform with the simulation-based notion of security used by the cryptographic community. In particular, previous arguments as to why this condition provides security do not consider parallel composition of protocols. We remedy this situation by giving the first complete proof that when combined with a notion of correctness, it implies cryptographic (simulation-based) security for QKD. To do this, we first revisit the notion of simulatable security necessary for a general protocol to be usable in a larger cryptographic context, and derive the corresponding security criterion for QKD. We then prove that the known notions of secrecy and correctness are sufficient to achieve this security criterion. We also illustrate the composition of various protocols with QKD with several examples.

The ability to reduce proofs of quantum information processing tasks from any permutation in-variant state to a de-Finetti state, that is, a convex combination of i.i.d. states, is useful in several tasks, such as cryptographic quantum protocols and quantum tomography. It is thus interesting to see whether such de-Finetti type theorems are unique for quantum theory or can be proven for more general theories. We prove that this can indeed be done under the framework of conditional probability distributions. That is, a physical system is described by a conditional probability distribution PA|X where X denotes the possible measurements and A the possible outcomes. For such systems we prove a post selection theorem which states that any permutation invariant system PA|X can be post selected by a measurement of a de-Finetti type system with high enough probability. We use this theorem to simplify security proofs of non-signalling cryptographic protocols.

A natural definition for a process to be truly random is that its outcome is not predictable from any information available before the process has been started. The advantage of using quantum systems for random number generation compared to classical approaches lies in the fact that the unpredictability of the randomness can be proven based on physical principles. In practice however, due to imperfections of the devices, the resulting raw randomness also depends on classical noise and therefore does not fulfil this definition either. Here we provide a framework for generating almost perfect true randomness using noisy devices by appropriate post-processing (hashing) of the raw randomness. Compared to previous work on random number generators (RNGs), we take this noise into account as side information, which is necessary to meet the above definition of true randomness. Our approach assumes that the process generating the raw randomness is correctly described by a quantum model. Compared to device- independent randomness expansion, this has the advantage of being practical (it is applicable to commercially available devices) and does not require pre-existing randomness. We stress, however, that our results do not rely on any completeness assumption regarding the model or quantum theory. We illustrate our proposal for a Quantum Random Number Generator (QRNG) based on a beam splitter and show how the post-processing procedure used in some of the current devices can be improved.

Removing assumptions about devices and signals from quantum cryptography protocols is an important task. Often it is assumed that measurements are memoryless and each signal is measured independently. We aim to remove this assumption by considering a related problem involving what we call quantum exams: First assume a student has a quantum memory which has an encoding of a classical string. Consider that the student is asked to produce a small subset of the string (i.e. and exam), and then is asked for another subset of the string. If the student can make a good estimate in the first exam, he should be able to also make a good estimate in the second exam. We examine this problem in the case of a classical or quantum memory for the student, and its relation to quantum cryptography.

Delegating difficult computations to remote large computation facilities, with appropriate security guarantees, is a possible solution for the ever-growing needs of personal computing power. For delegated computation protocols to be usable in a larger context—or simply to securely run two protocols in parallel—the security definitions need to be composable. Here, we define composable security for delegated quantum computation, and prove that several known protocols are composable, including Broadbent, Fitzsimons and Kashefi’s Universal Blind Quantum Computation protocol.We distinguish between protocols which provide only blindness—the computation is hidden from the server—and those that are also verifiable—the client can check that it has received the correct result. We show that the composable security definition capturing both these notions can be reduced to a combination of two distinct stand-alone security definitions.