The emergence of quantum theory at the beginning of 20$-th$ century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a few, that could never have been realised using classical systems. One such application that has attracted considerable attention lately is device-independent (DI) certification of composite quantum systems. The basic idea behind it is to treat a given device as a black box that given some input generates an output, and then to verify whether it works as expected by only studying the statistics generated by this device. The novelty of these certification schemes lies in the fact that one can almost completely characterise the device (up to certain equivalences) under minimal physically well-motivated assumptions such as that the device is described using quantum theory. The resource required in most of these certification schemes is quantum non-locality. In this thesis, we construct schemes to device-independently certify quantum states and quantum measurements in Hilbert spaces of arbitrary dimension along with the optimal amount randomness that one can extract from any quantum system of arbitrary dimension.
The emergence of quantum theory at the beginning of 20−th century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a few, that could never have been realised using classical systems. One such application that has attracted considerable attention lately is device-independent (DI) certification of composite quantum systems. The basic idea behind it is to treat a given device as a black box that given some input generates an output, and then to verify whether it works as expected by only studying the statistics generated by this device. The novelty of these certification schemes lies in the fact that one can almost completely characterise the device (up to certain equivalences) under minimal physically well-motivated assumptions such as that the device is described using quantum theory. The resource required in most of these certification schemes is quantum non-locality. In this thesis, we construct schemes to device-independently certify quantum states and quantum measurements in Hilbert spaces of arbitrary dimension along with the optimal amount randomness that one can extract from any quantum system of arbitrary dimension.
The question of certifying quantum nonlocality under a relaxation of the assumptions in the Bell theorem has gained traction, with potential for device-independent applications under weak seeds and cross-talk. Recently, it was shown that quantum nonlocality can be certified even under a simultaneous arbitrary (but not full) relaxation of the assumptions of Measurement Independence (MI) and Parameter Independence (PI), using states of local dimension d=poly((1−ε)−1) for an ε∈[0,1)-relaxation. Here, we derive three results strengthening the state-of-art. Firstly, we show that states of constant local dimension d are already sufficient to certify quantum nonlocality under arbitrary MI and PI relaxation, albeit in a non-robust manner. Secondly, and as a theoretical paradigm to derive the above, we introduce the notion of \textit{measurement-dependent parameter-dependent locality} as the set of input-output behaviors under simultaneous relaxations of measurement and parameter independence. We provide a rigorous characterisation of the vertices of the polytope of joint input-output behaviors that obey a μ-relaxation of MI and ε-relaxation of PI. We highlight a relation between nonlocality certification under PI relaxation and that under detection inefficiencies by pointing out alternative extremal correlations to the Eberhard correlations that also allow to achieve detection efficiency of η=2/3 in the two-input scenario. Finally, we study the implication of the relaxed assumptions for device-independent randomness certification. We analytically derive the quantum guessing probability for one player's outcomes in the CHSH Bell test, as a function of the noise in the test as well as of a leakage of an average amount of I(X:B)<1 bits of input information per measurement round.
Nonlocal correlations are useful for device-independent (DI) randomness certification (P ironio S. et al. , Nature (London) , 464 (2010) 1021). The advantage of this DI protocol over the conventional quantum protocol is that randomness can be certified even when experimental apparatuses are not trusted. Quantum entanglement is the necessary physical source for the nonlocal correlation required for such DI task. However, nonlocality and entanglement are distinct concepts. There exist entangled states which produce no nonlocal correlation and hence are not useful for the DI randomness certification task. Here we introduce the measurement-device–independent randomness certification task where one has trusted quantum state preparation devices but the mesurement devices are completely unspecified. Interestingly we show that there exist entangled states, with local description, that are a useful resource in such task but are useless in the corresponding DI scenario.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e., we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, ie, we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
The device-independent formalism is a set of tools to analyze experimental data and infer properties about systems, while avoiding almost any assumption about the functioning of devices. It has found applications both in fundamental and applied physics: some examples are the characterization of quantum nonlocality and information protocols for secure cryptography or randomness generation. This thesis contains novel results on these topics and also new applications such as deviceindependent test for dimensionality. After an introduction to the field, the thesis is divided in four parts. In the first we study device-independent tests for classical and quantum dimensionality. We investigate a scenario with a source and a measurement device. The goal is to infer, solely from the measurement statistics, the dimensionality required to describe the system. To this end, we exploit the concept of dimension witnesses. These are functions of the measurement statistics whose value allows one to bound the dimension. We study also the robustness of our tests in more realistic experimental situations, in which devices are affected by noise and losses. Lastly, we report on an experimental implementation of dimension witnesses. We conducted the experiment on photons manipulated in polarization and orbital angular momentum. This allowed us to generate ensembles of classical and quantum systems of dimension up to four. We then certified their dimension as well as its quantum nature by using dimension witnesses. The second part focuses on nonlocality. The local content is a nonlocality quantifier that represents the fraction of events that admit a local description. We focus on systems that exhibit, in that sense, maximal nonlocality. By exploiting the link between Kochen-Specker theorems and nonlocality, we derive a systematic recipe to construct maximally nonlocal correlations. We report on the experimental implementation of correlations with a high degree on nonlocality in comparison with all previous experiments on nonlocality. We also study maximally nonlocal correlations in the multipartite setting, and show that the so-called GHZ-state can be used to obtain correlations suitable for multipartite information protocols, such as secret-sharing. The third part studies nonlocality from an operational perspective. We study the set of operations that do not create nonlocality and characterize nonlocality as a resource theory. Our framework is consistent with the canonical definitions of nonlocality in the bipartite setting. However, we find that the well-established definition of multipartite nonlocality is inconsistent with the operational framework. We derive and analyze alternative definitions of multipartite nonlocality to recover consistency. Furthermore, the novel definitions of multipartite nonlocality allows us to analyze the validity of information principles to bound quantum correlations. We show that `information causality' and `non-trivial communication complexity' are insufficient to characterize the set of quantum correlations. In the fourth part we present the first quantum protocol attaining full randomness amplification. The protocol uses as input a source of imperfect random bits and produces full random bits by exploiting nonlocality. Randomness amplification is impossible in the classical regime and it was known to be possible with quantum system only if the initial source was almost fully random. Here, we prove that full randomness can indeed be certified using quantum non-locality under the minimal possible assumptions: the existence of a source of arbitrarily weak (but non-zero) randomness and the impossibility of instantaneous signaling. This implies that one is left with a strict dichotomic choice regarding randomness: either our world is fully deterministic or there exist events in nature that are fully random.
The onset of the era of fully-programmable error-corrected quantum computers will be marked by major breakthroughs in all areas of science and engineering. These devices promise to have significant technological and societal impact, notable examples being the analysis of big data through better machine learning algorithms and the design of new materials. Nevertheless, the capacity of quantum computers to faithfully implement quantum algorithms relies crucially on their ability to prepare specific high-dimensional and high-purity quantum states, together with suitable quantum measurements. Thus, the unambiguous certification of these requirements without assumptions on the inner workings of the quantum computer is critical to the development of trusted quantum processors. One of the most important approaches for benchmarking quantum devices is through the mechanism of self-testing that requires a pair of entangled non-communicating quantum devices. Nevertheless, although computation typically happens in a localized fashion, no local self-testing scheme is known to benchmark high dimensional states and measurements. Here, we show that the quantum self-testing paradigm can be employed to an individual quantum computer that is modelled as a programmable black box by introducing a noise-tolerant certification scheme. We substantiate the applicability of our scheme by providing a family of outcome statistics whose observation certifies that the computer is producing specific high-dimensional quantum states and implementing specific measurements.