Quantum violations in the Instrumental scenario and their relations to the Bell scenario

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.Comment: 12 pages, 3 figures. Comments welcome! v4: published version in Quantum journa

Impossibility of adversarial self-testing and secure sampling

Self-testing is the task where spatially separated Alice and Bob cooperate to deduce the inner workings of untrusted quantum devices by interacting with them in a classical manner. We examine the task above where Alice and Bob do not trust each other which we call adversarial self-testing. We show that adversarial self-testing implies secure sampling -- a task that we introduce where mistrustful Alice and Bob wish to sample from a joint probability distribution with the guarantee that an honest party's marginal is not biased. By extending impossibility results in two-party quantum cryptography, we give a simple proof that both of these tasks are impossible in all but trivial settings.Comment: 6 pages, 3 Figure

Practical self-testing quantum random number generator based on an energy bound

We present a scheme for a self-testing quantum random number generator. Compared to the fully device-independent model, our scheme requires an extra natural assumption, namely that the mean energy per signal is bounded. The scheme is self-testing, as it allows the user to verify in real-time the correct functioning of the setup, hence guaranteeing the continuous generation of certified random bits. Based on a prepare-and-measure setup, our scheme is practical, and we implement it using only off-the-shelf optical components. The randomness generation rate is 1.25 Mbits/s, comparable to commercial solutions. Overall, we believe that this scheme achieves a promising trade-off between the required assumptions, ease-of-implementation and performance

Semi-device-independent framework based on natural physical assumptions

The semi-device-independent approach provides a framework for prepare-and-measure quantum protocols using devices whose behavior must not be characterized nor trusted, except for a single assumption on the dimension of the Hilbert space characterizing the quantum carriers. Here, we propose instead to constrain the quantum carriers through a bound on the mean value of a well-chosen observable. This modified assumption is physically better motivated than a dimension bound and closer to the description of actual experiments. In particular, we consider quantum optical schemes where the source emits quantum states described in an infinite-dimensional Fock space and model our assumption as an upper bound on the average photon number in the emitted states. We characterize the set of correlations that may be exhibited in the simplest possible scenario compatible with our new framework, based on two energy-constrained state preparations and a two-outcome measurement. Interestingly, we uncover the existence of quantum correlations exceeding the set of classical correlations that can be produced by devices behaving in a purely pre-determined fashion (possibly including shared randomness). This feature suggests immediate applications to certified randomness generation. Along this line, we analyze the achievable correlations in several prepare-and-measure optical schemes with a mean photon number constraint and demonstrate that they allow for the generation of certified randomness. Our simplest optical scheme works by the on-off keying of an attenuated laser source followed by photocounting. It opens the path to more sophisticated energy-constrained semi-device-independent quantum cryptography protocols, such as quantum key distribution.Comment: 26 pages, 10 figure

Semi-device-independent framework based on natural physical assumptions

info:eu-repo/semantics/nonPublishe

Quantum Cryptography with Partially Trusted Devices

The aim of this thesis is the introduction of new practical Quantum Random Number Generators and new mathematical techniques to certify the random nature of the numbers, based only on a partial characterisation of the devices. Random numbers have a lot of applications, going from mathematical algorithms and betting games to cryptographic protocols, where random keys are a basic premise for constructing protocols. Random Number Generators of the Quantum type have the advantage that they rely on truly random processes, which are guaranteed to be unpredictable by the laws of physics. This makes them in principle more safe than classical hardware generators and pseudo-random algorithms. In the first part of the thesis, we focus of the task of certifying randomness. We introduce a new framework for certifying generators based on quantum optics and that follow a Prepare-and-Measure setup consisting of a source and a measurement device, such as a laser and a single photon detector. Our framework is called semi-Device-Independent, because the device is left largely uncharacterised, as no assumption is made on the source and the measurement device, except for a single physical assumption on the mean photon number (or the energy) of the states prepared by the source. This approach is very secure and robust because any malfunctioning or imperfections in the generator, such additional classical noise, are automatically taken into account as long as the energy assumption is satisfied. We show that, under an energy constraint, there is a fundamental relation between the amount of correlation between the two devices and the amount of randomness produced during the measurement. We establish this by considering all possible underlying quantum models of the devices, that satisfy the mean photon number constraint. We demonstrate that certain strong correlations indeed cannot be reproduced by an underlying deterministic model and show how to compute the amount of randomness in these cases. We then prove the security of a random number generation protocol and demonstrate it in a proof-of-principle experiment. In the second part of the thesis, we study the Instrumental scenario, which is a Device-Independent framework based on causal constraints. We derive the existence of analogues to Bell-inequalities which bound the set of classical correlations and we show that they can be violated by quantum devices. At a more fundamental level, the Instrumental scenario is interesting because it is the simplest causal scenario admitting a separation between classical and quantum correlations.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe