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.
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.
By certifying quantum operations from measurement statistics directly, without any assumption on the internal workings of the devices involved, self-testing enables a uniquely reliable identification of quantum objects. While such device-independent characterization has been shown to be possible for states, measurements and channels, it has so far not been extended to quantum supermaps -- operations that act on quantum channels themselves and can combine them in either a well-defined causal order or also, remarkably, in an indefinite causal order. Here we show that quantum supermaps can be identified device-independently. Specifically, we obtain two levels of certification, depending on the network structure of the experiment: when each slot of the supermap accepts a single uncharacterized black box, identification up to local embedding combs is obtained; when several black boxes are inserted within each slot, identification up to local extracting and injecting maps is achieved. We illustrate our approach on four examples -- the identity comb, a bit-flip error-correcting comb, the comb describing Grover's algorithm, and the quantum switch -- providing in particular the first self-test of both a quantum algorithmic comb and a causally indefinite quantum process. Notably, in the latter case, this provides a new way to certify causal indefiniteness in a device-independent manner.
Quantum information has the potential to disrupt the present computational landscape. Much of this potential rests on the existence of efficient quantum algorithms for classically intractable problems and of quantum cryptographic protocols for tasks that are provably impossible to realize classically. At the heart of many quantum advantages is one of the most counterintuitive features of quantum mechanics, known as entanglement. The central motivating question of this thesis is the following: if quantum devices will perform tasks that are beyond the reach of classical devices, can we hope to certify that they are performing these tasks correctly? Bell's theorem, a landmark result in physics, provides a partial answer to this question: it asserts that measurements on spatially isolated, but entangled, particles can result in outcomes that are correlated in a way that cannot be explained by any local hidden variable theory (such as Newtonian physics). A direct operational consequence of this theorem is that one can devise a statistical test to certify the presence of entanglement (and hence of genuine quantumness). Remarkably, nature allows us to take this certification one step further: in some cases, the correlation of measurement outcomes is sufficient to single out a unique quantum setup compatible with this correlation. This phenomenon is often referred to as self-testing, and is the central topic of this thesis. In the first part of this thesis, we review the basic terminology and results in the theory of self-testing. We then explore a concrete application to the problem of verifiably delegating a quantum computation. Our main technical contribution is a test that robustly certifies products of single-qubit Clifford measurements on many EPR pairs. We employ this test to obtain a protocol which allows a classical user to verifiably delegate her quantum computation to two spatially isolated quantum servers. The overall complexity of our protocol is near-optimal, requiring resources that scale almost linearly in the size of the circuit being delegated. In the second part of this thesis, the driving question is the following: what is the class of quantum states and measurements that can be certified through self-testing? Does self-testing only apply to a few special cases, like EPR pairs or copies of EPR pairs, or are these instances of a more general phenomenon? One of the main results of this thesis is that we settle this question for the case of bipartite states. We show the existence of a self-testing correlation for any pure bipartite entangled state of any finite local dimension. We then move on to explore the multipartite case, and we show that a significantly larger class of states can be self-tested than was previously known. This includes all multipartite partially entangled GHZ states, and more generally all multipartite qudit states which admit a Schmidt decomposition. In the final part of this thesis, we explore connections of the theory of self-testing to basic questions about entanglement and quantum correlation sets. In particular, we set out to understand the expressive power of infinite-dimensional quantum systems. We consider two questions: can spatially isolated quantum systems of infinite dimension produce correlations that are unattainable by finite-dimensional systems? Does there exist a correlation that cannot be attained exactly by spatially isolated quantum systems (not even infinite-dimensional ones), but can be approximated arbitrarily well by a sequence of finite or infinite-dimensional systems? The first question was posed by Tsirelson in 1993, and its answer has been elusive. One of the main results of this thesis is a resolution of this question. The second question is better known as the "non-closure of the set of quantum correlations", and was answered affirmatively in a breakthrough of Slofstra. We give a new elementary proof of this result which leverages one of our self-testing results and a phenomenon known as embezzlement.
Abstract Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d -outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, log2d log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.
Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.
It has been known that all bipartite pure quantum states can be certified by quantum self-testing, i.e., any such states can be pinned down completely based on the statistics produced by local quantum measurements. A notable feature of quantum self-testing is that the conclusions remain reliable even when the quantum measurements involved are untrusted, where quantum nonlocality is crucial. This necessitates that each party conducts at least two different quantum measurements to produce the desired correlation. Here, we prove that when the underlying Hilbert space dimension is known beforehand, which is very common in quantum experiments, an arbitrary d×d bipartite pure state can be certified completely (up to local unitaries) by a certain correlation generated with a single measurement setting on each party, where each measurement yields only 2d or even d+1 outcomes. We also prove the robustness of our protocols to quantum noises and experimental imperfections. Compared with quantum self-testing, our protocols do not hinge on quantum nonlocality and are much more efficient, yet they maintain the essential feature of not requiring additional assumptions about the quantum devices involved. This advancement could offer significant convenience when certifying bipartite quantum states using untrusted quantum devices in future quantum industries.
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.