Archive ouverte UNIGE | last documents for author 'Sébastien Karl Gérard Designolle'https://archive-ouverte.unige.ch/Latest objects deposited in the Archive ouverte UNIGE for author 'Sébastien Karl Gérard Designolle'engIncompatibility of high-dimensional quantum measurementshttps://archive-ouverte.unige.ch/unige:158942https://archive-ouverte.unige.ch/unige:158942Théorie de l'infiniment petit, la mécanique quantique surprend depuis près d'un siècle et ses contre-intuitives prédictions en ont fait le renom. Ainsi, toute mesure effectuée sur un système quantique est intrinsèquement perturbante et l'état en ressort généralement modifié. Bouleversé par une première mesure, il se peut alors que ce système donne un résultat faussé pour une seconde : on parle de mesures incompatibles, dont un exemple célèbre est donné par les relations d'incertitudes d'Heisenberg qui limitent la précision simultanée sur la position et l'impulsion. Examiner de façon quantitative cette propriété dans le cas de systèmes disposant d'un nombre fini mais potentiellement grand de degrés de libertés a été l'un des objectifs de ma thèse. Rares étaient les résultats au-delà du bit quantique, en partie du fait de la difficulté à visualiser les états de grande dimension ainsi que de l'explosion du nombre de paramètres. Néanmoins, en développant des méthodes calculatoires universelles ou en exploitant des structures plus abstraites mais se prêtant bien à la généralisation, j'ai pu commencer à débroussailler la jungle touffue des hautes dimensions, dont la luxuriance a souvent pu être mise à profit. Aussi ces résultats ont-ils naturellement trouvé des conséquences expérimentales dans le domaine du pilotage quantique, applications que j'évoque pour finir. Ce manuscrit met en résonance plusieurs articles scientifiques publiés au cours de ma thèse. La fluide articulation des différents résultats a souvent impliqué une sélection du contenu exposé ainsi qu'une réduction du niveau de détail. En appendice de cette thèse se trouvent les articles originaux parmi lesquels pourront être trouvés l'ensemble des preuves, des résultats complémentaires, et les publications non présentées.Wed, 16 Feb 2022 15:12:25 +0100Experimental relativistic zero-knowledge proofshttps://archive-ouverte.unige.ch/unige:156269https://archive-ouverte.unige.ch/unige:156269Protecting secrets is a key challenge in our contemporary information-based era. In common situations, however, revealing secrets appears unavoidable, for instance, when identifying oneself in a bank to retrieve money. In turn, this may have highly undesirable consequences in the unlikely, yet not unrealistic, case where the bank's security gets compromised. This naturally raises the question of whether disclosing secrets is fundamentally necessary for identifying oneself, or more generally for proving a statement to be correct. Developments in computer science provide an elegant solution via the concept of zero-knowledge proofs: a prover can convince a verifier of the validity of a certain statement without facilitating the elaboration of a proof at all. In this work, we report the experimental realisation of such a zero-knowledge protocol involving two separated verifier-prover pairs. Security is enforced via the physical principle of special relativity, and no computational assumption (such as the existence of one-way functions) is required. Our implementation exclusively relies on off-the-shelf equipment and works at both short (60 m) and long distances (400 m) in about one second. This demonstrates the practical potential of multi-prover zero-knowledge protocols, promising for identification tasks and blockchain-based applications such as cryptocurrencies or smart contracts.Wed, 10 Nov 2021 15:21:05 +0100Quantum entanglement in the triangle networkhttps://archive-ouverte.unige.ch/unige:154981https://archive-ouverte.unige.ch/unige:154981Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum states and their entanglement. We address the questions of which states can be prepared in the so-called triangle network, consisting of three nodes connected pairwise by three sources. We derive necessary criteria for a state to be preparable in such a network, considering both the cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and non-trivial constraints on the set of preparable states, fundamentally different from the standard characterization of multipartite quantum entanglement.Mon, 27 Sep 2021 14:22:32 +0200Genuine high-dimensional quantum steeringhttps://archive-ouverte.unige.ch/unige:154979https://archive-ouverte.unige.ch/unige:154979High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalise and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities, the violation of which guarantees the presence of genuine high-dimensional steering, and hence certifies a lower bound on the Schmidt number in a one-sided device-independent setting. We report the experimental violation of these inequalities using macro-pixel photon-pair entanglement certifying genuine high-dimensional steering. In particular, using an entangled state in dimension $d=31$, our data certifies a minimum Schmidt number of $n=15$.Mon, 27 Sep 2021 14:20:08 +0200Set coherence: basis-independent quantification of quantum coherencehttps://archive-ouverte.unige.ch/unige:154978https://archive-ouverte.unige.ch/unige:154978The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set coherence for characterising the coherence of a set of quantum systems in a basis-independent way. We construct measures for quantifying set coherence of sets of quantum states as well as quantum measurements. These measures feature an operational meaning in terms of discrimination games and capture precisely the advantage offered by a given set over incoherent ones. Along the way, we also connect the notion of set coherence to various resource-theoretic approaches recently developed for quantum systems.Mon, 27 Sep 2021 14:18:55 +0200Quantum measurement incompatibility in subspaceshttps://archive-ouverte.unige.ch/unige:150406https://archive-ouverte.unige.ch/unige:150406We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.Mon, 15 Mar 2021 11:21:42 +0100Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steeringhttps://archive-ouverte.unige.ch/unige:127284https://archive-ouverte.unige.ch/unige:127284A sequential steering scenario is investigated, where multiple Bobs aim at demonstrating steering using successively the same half of an entangled quantum state. With isotropic entangled states of local dimension d, the number of Bobs that can steer Alice is found to be NBob∼d/logd, thus leading to an arbitrary large number of successive instances of steering with independently chosen and unbiased inputs. This scaling is achieved when considering a general class of measurements along orthonormal bases, as well as complete sets of mutually unbiased bases. Finally, we show that similar results can be obtained in an anonymous sequential scenario, where none of the Bobs know their position in the sequence.Tue, 03 Dec 2019 14:42:05 +0100Quantifying Measurement Incompatibility of Mutually Unbiased Baseshttps://archive-ouverte.unige.ch/unige:127278https://archive-ouverte.unige.ch/unige:127278Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k=d+1 MUB (given d is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.Tue, 03 Dec 2019 14:31:28 +0100Algorithmic construction of local models for entangled quantum states: Optimization for two-qubit stateshttps://archive-ouverte.unige.ch/unige:127275https://archive-ouverte.unige.ch/unige:127275The correlations of certain entangled quantum states can be fully reproduced via a local model. We discuss in detail the practical implementation of an algorithm for constructing local models for entangled states, recently introduced by Hirsch et al. [Phys. Rev. Lett. 117, 190402 (2016)] and Cavalcanti et al. [Phys. Rev. Lett. 117, 190401 (2016)]. The method allows one to construct both local hidden state (LHS) and local hidden variable (LHV) models, and can be applied to arbitrary entangled states in principle. Here we develop an improved implementation of the algorithm, discussing the optimization of the free parameters. For the case of two-qubit states, we design a ready-to-use optimized procedure. This allows us to construct LHS models (for projective measurements) that are almost optimal, as we show for Bell diagonal states, for which the optimal model has recently been derived. Finally, we show how to construct fully analytical local models, based on the output of the convex optimization procedure.Tue, 03 Dec 2019 14:16:51 +0100Quantification of multidimensional entanglement stored in a crystalhttps://archive-ouverte.unige.ch/unige:112336https://archive-ouverte.unige.ch/unige:112336The use of multidimensional entanglement opens new perspectives for quantum information processing. However, an important challenge in practice is to certify and characterize multidimensional entanglement from measurement data that are typically limited. Here, we report the certification and quantification of two-photon multidimensional energy-time entanglement between many temporal modes, after one photon has been stored in a crystal. We develop a method for entanglement quantification which makes use of only sparse data obtained with limited resources. This allows us to efficiently certify an entanglement of formation of 1.18 ebits after performing quantum storage. The theoretical methods we develop can be readily extended to a wide range of experimental platforms, while our experimental results demonstrate the suitability of energy-time multidimensional entanglement for a quantum repeater architecture.Fri, 14 Dec 2018 15:19:28 +0100