Metrology is an important area of new quantum technologies, with applications in gravitational and magnetic field sensors, accelerometers and gyrometers, among others. In this lecture, a review of quantum metrology methods will be presented and recent results involving noisy systems will be discussed, with a large quantum advantage compared to classical estimation methods.

I will show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This time translation effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes that are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. The possible time translations which once can effect on multiple target systems through a scattering protocol of fixed duration are precisely those that satisfy the following rules: a) (evolution) time cannot be created; b) time can be transferred between systems with the same free Hamiltonian at no cost; c) time can be inverted, but at a cost: rewinding a target system by T seconds requires disposing of (D-1)T seconds of time, where D is the Hilbert space dimension of the target.

Nature violates Bell inequalities. However, it is not clear why this violation occurs and what does it mean. There are several possibilities: (i) It could indicate that measurement outcomes are governed by nonlocal hidden variables. (ii) It could indicate that measurement outcomes are governed by local hidden variables and measurements depend on the hidden variables. (iii) It could indicate that neither measurements nor measurement outcomes are governed in any way by hidden variables. Here, I examine these possibilities under the light of some recent developments in the program of deriving from fundamental principles the sets of quantum correlations for Bell and Kochen-Specker contextuality scenarios and show that the option that, at first sight, has less explanatory power is the one that actually explains more.

Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements from this. In other words, it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output statistics and is known to be possible in several cases. In this talk, I will introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, I will ask whether within a particular network there are tasks that can only be performed in theories that have the same correlations as quantum mechanics. I will introduce two candidate tasks, both adaptations of the usual CHSH-Bell-test in a larger network and will show how they can be used to rule out theories. The first one can be used to rule out a variety of theories including the theory of box-world, which is based on a state space that includes PR-boxes. The second one recently allowed us to rule out quantum theory over real Hilbert spaces as incompatible with our experimental observations. Our work goes beyond previous approaches that usually compare different theories according to their properties, often by imposing postulates. By finding self-tests we design more objective, experimentally verifiable procedures to rule out beyond-quantum-theories.

Semidefinite Programming (SDP) is a class of convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization, machine learning and operational research. In this talk, I will discuss how SDP can be used to address two major challenges in quantum computing research: near-term quantum advantage and device certification. Towards the first challenge, I will discuss how to design noisy intermediate-scale quantum (NISQ) algorithms, that bypass the local minima problem, one of the central problems faced by variational quantum algorithms. As an example, I will discuss a NISQ eigensolver that does not suffer from any trainability problem, such as the barren plateau or local minima problem. In the second part of the talk, I will discuss how can one use SDPs to give theoretical guarantees regarding the inner functioning of quantum devices under minimal assumptions. In particular, I will discuss the strategies to prove self-testing statements using tools from semidefinite programming and graph theory.

**References:**

Kishor Bharti, Tobias Haug, Vlatko Vedral, Leong-Chuan Kwek, arXiv:2106.03891

Kishor Bharti, Maharshi Ray, Antonios Varvitsiotis, Naqueeb Ahmad Warsi, Adán Cabello, Leong-Chuan Kwek, Phys. Rev. Lett. 122, 250403

Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, Alán Aspuru-Guzik, Rev. Mod. Phys. 94, 015004

Quantum incompatibility is a fundamental trait of quantum theory. It can be traced back to Heisenberg’s uncertainty principle, but is nowadays understood as a more general feature with diverse manifestations. It is related to many important quantum phenomena, such as steering, non-locality and contextuality. In this talk, I explain how three basic facts of quantum theory—the no-cloning theorem, no-information-without-disturbance theorem, and the existence of complementary observables—naturally lead to a unified general concept of incompatibility of quantum devices. I present some examples of compatible and incompatible collections of devices, and discuss the most essential properties of the (in)compatibility relation.

The combination of entanglement and quantum communication is the most general communication resource enabled by quantum theory. Its power is well known due to the fame of quantum dense coding. Surprisingly, 30 years later, beyond the information-theoretic task of encoding and decoding messages (quantum channel capacities), almost nothing is known about the general predictions of quantum theory in these scenarios. In this talk, I give an overview of our recent ground-up investigations of correlations in entanglement-assisted prepare-and-measure scenarios, and also discuss some of the open problems that lay ahead.

Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the post-quantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two observers (of classical systems) cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for observers of quantum systems, while we construct examples of (post-quantum) no-signaling boxes where observers can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.

One of the key studies within quantum theory is to understand exactly how the quantum and classical worlds differ from one another. In this talk I will focus on the notion of generalised noncontextuality, which cleanly delineates between those theories which can be thought of as admitting of a classical explanation, and those, such as quantum theory, that cannot. In recent work we have shown how this notion can be understood within the framework of generalised probabilistic theories, which leads to an intuitive, geometric, account of generalised noncontextuality. By doing so we can prove a collection of surprising results, not least of all, that it is possible to have proofs of contextuality that do not use any incompatible measurements.

In order to develop a resource theory of nonlocality one must first isolate that essential physical property which underlies Bell inequality violation. We propose nonclassicality of a causal common cause as that property, which implies local operations and shared randomness (LOSR) as the choice of free operations. In this talk I’ll explore a myriad after happy conceptual clarifications that follow from electing to quantify nonlocality via LOSR. Highlights include the resolution of anomalies between nonlocality and entanglement, a linear program formulation for assessing convertibility between nonsignalling boxes, conceptual cleanup regarding self-testing, and a causally-motivated definition of multipartiteness relative to LOSR. The latter connects this work to foundational quantum (and GPT) causal inference problems in the notorious triangle scenario.

Based primarily on the recently updated Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory, as well as the new No Bipartite-Nonlocal Causal Theory Can Explain Nature’s Correlations, and Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes.

**Authors:** William F. Braasch Jr. and William K. Wootters

**Abstract:** In a 2016 paper, Rob Spekkens presented an “epistemically restricted classical theory” based on discrete phase space. The theory has many features in common with quantum theory, but it cannot imitate quantum theory perfectly because it is noncontextual.

Here we start with a theory like the one Spekkens proposed, but we add a crucial ingredient in order to recover quantum theory itself for a certain class of systems. The extra ingredient is to consider all the possible classical accounts of a given experiment, and to combine the predictions of these accounts by the following rule: the nonrandom part of the quantum prediction is given by the sum of the nonrandom parts of the classical predictions.

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present ystematic ethods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of andomized measurements. Second, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework. Finally, we analyze the resources needed for a statistically significant test

**References:**

S. Imai, N Wyderka, A. Ketterer, O. Gühne, arXiv:2010.08372

A. Ketterer, S. Imai, N. Wyderka, O. Gühne, arXiv:2012.12176

Because “quantum” was not complex enough, in this talk I will introduce you to “post-quantum”. We will discuss how current non-classical phenomena, such as those observed in Bell and Steering scenarios, have room to accommodate possible physical theories we have yet to grasp. I will also introduce you to mathematical frameworks to explore toy physical theories (which may supersede quantum) and manifestations of post-quantum phenomena. The aim is to provide you with sufficient context so you can pursue your desired journey into quantum foundations.

Random Access Code (RAC) is a protocol in which some information is encoded into a system by sender and the receiver attempts to decode part of it. It so happens that quantum systems have an advantage over the classical in the terms of probability to decode the information correctly. In this talk I will present a whole zoo of different RAC variants. They have very different properties and applications ranging from practical information processing problems like quantum key distribution to foundations of physics to pure mathematics. I’ll discuss these applications.

Physics and its philosophy are full of puzzles related to the first-person perspective of observers: Wigner’s friend, the Boltzmann brain problem, Parfit’s teletransportation paradox and many others. In my talk, I argue that there are basically only two options: first, deliberately declare those problems as outside the scope of science. Second, explore an alternative approach to the foundations of physics in which not an “external world”, but a mathematical notion of “mind” is primary. I show how such an approach can be rigorously formulated, how it reproduces our usual picture of the world to excellent approximation, and how it can solve the aforementioned problems and more in one stroke.

Based on arXiv:1712.01826 / Quantum 4, 301 (2020).