Quantum Foundations

In this talk, I will discuss correlations that can be generated by performing local measurements on bipartite quantum systems. I'll present an algebraic characterization of the set of quantum correlations which allows us to identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a quantum correlation. I will then discuss some examples showing the tightness of our lower bound. Also, the algebraic characterization can be used to express the set of quantum correlations as the projection of an affine section of the cone of completely positive semidefinite matrices. Using this, we identify a semidefinite programming outer approximation to the set of quantum correlations which is contained in the first level of the Navascués, Pironio and Acín hierarchy, and a linear conic programming problem formulating exactly the quantum value of a nonlocal game. Time permitting, I will discuss other consequences of these conic formulations and some interesting special cases.

This talk is based on work with Antonios Varvitsiotis and Zhaohui Wei, arXiv:1507.00213 and arXiv:1506.07297.

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like the concept of perfectly independent copies of states used to derive conversion rates. As these idealizations are impossible to implement in practice, such results may be of little consequence for experimentalists.

In this talk I introduce tools to quantify realistic descriptions of resources, applicable for example when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out.

Some resources, like entanglement, can be characterized in terms of copies of local states: we generalize this with operational ways to describe composition and copies of realistic resources, without assuming a tensor product structure.  For others, like thermodynamic work, value is seen as a real function on physical states, like the height of a weight. While value is often expected to behave linearly, that simplification excludes many real-life resources: for example, the operational value of money, in terms of what can be done with it, is hardly linear on the amount of coin, and even has catalytic aspects above certain thresholds. We characterize resources that behave linearly and those that allow for investments - in the extreme, catalytic resources.

This work is an application of the framework introduced in arXiv:1511.08818.

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space.  Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms.  We present a theorem to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of possibilities.  This serves as a kind of "no-go" theorem for these alternative, or generalized, probability theories.

Time in quantum mechanics has duly received a lot of attention over the years. Perfect clocks which can turn on/off a particular interaction at a precise time that have been proposed only exist in infinite dimensions and have unphysical Hamiltonians (their spectrum is unbounded from below). It was this observation which led many to conclude that an operator for time cannot exist in quantum mechanics. Here, we prove rigorous results about the accuracy of finite dimensional clocks and show that they can well approximate their infinite dimensional counterparts under the right conditions.

The talk first offers a brief assessment of the realist and nonrealist understanding of quantum theory, in relation to the role of probability and statistics there from the perspective of quantum information theory, in part in view of several recent developments in quantum information theory in the work of M. G. D’Ariano and L. Hardy, among others. It then argues that what defines quantum theory, both quantum mechanics and quantum field theory, most essentially, including as concerns realism or the lack thereof and the probability and statistics, is a new (vs. classical physics or relativity) role of technology in quantum physics. This role was first considered by Bohr in his analysis of the fundamental role of measuring instruments in the constitution of quantum phenomena, which, he argued, is responsible for the difficulties of providing a realist description of quantum objects and their behavior, and, correlatively, for the irreducibly probabilistic or statistical nature of all quantum predictions. In this paper, I mean “technology” in a broader sense, akin to what the ancient Greeks called “tekhne” (“technique”). It refers the means by which we create new mental and material constructions, such as mathematical, scientific, or philosophical theories or works of art and architecture, or machines, and through which we interact with the world. I shall consider three forms of technology—mathematical, experimental, and digital. The relationships among them were crucial to the discovery of the Higgs boson, and, I argue, are likely to remain equally crucial, indeed unavoidable, in the future of physics, especially quantum physics.

The Reeh-Schlieder theorem says, roughly, that, in any reasonable quantum field theory,  for any bounded region of spacetime R, any state can be approximated arbitrarily closely by operating on the vacuum state (or any state of bounded energy) with operators formed by smearing polynomials in the field operators with functions having support in R.  This strikes many as counterintuitive, and Reinhard Werner has glossed the theorem as saying that “By acting on the vacuum with suitable operations in a terrestrial laboratory, an experimenter can create the Taj Mahal on (or even behind) the Moon!” This talk has two parts.  First, I hope to convince listeners that the theorem is not counterintuitive,  and that it follows immediately from facts that are already familiar fare to anyone who has digested the opening chapters of any standard introductory textbook of QFT.  In the second, I will discuss what we can learn from the theorem about how relativistic causality is implemented in quantum field theories.

In this talk we will discuss how C*-algebras can be identified and characterised in terms of certain cosheaves with self-action. The reason we are interested in such a study is it to try and give a rigorous mathematical derivation of the axioms of quantum theory. In particular, many of the standard axioms for C*-algebras have unclear physical and operational meaning, but by defining an equivalence of categories between C*-algebras and cosheaves with self-action, we believe that these axioms can acquire a clear operational meaning. So far, however, we have only managed to show that every C*-algebra becomes a cosheaf with self-action, but we don't know whether the converse holds as well. This work is done in collaboration with Tobias Fritz.

The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which is the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality.

However,  no intuitive  criterion  is available for determining  the compatibility of even two (generalized) observables, despite the overarching importance of this problem  and intensive efforts of many researchers over more than 80 years.

Here we introduce an information theoretic  paradigm together with an intuitive geometric picture for decoding incompatible observables,

starting from two simple ideas:   Every  observable can only provide

limited  information and   information is monotonic  under data

processing. By virtue of quantum estimation theory, we introduce a family of universal criteria for detecting incompatible observables and a natural measure of incompatibility, which are applicable to arbitrary number of arbitrary observables. Based on this framework, we derive a family of universal  measurement uncertainty relations, provide a simple information theoretic explanation of quantitative wave--particle duality, and offer new perspectives for understanding Bell nonlocality, contextuality, and quantum precision limit.

In this talk, I will explore a timeless interpretation of quantum mechanics of closed systems, solely in terms of path integrals in non-relativistic timeless configuration space. What prompts a fresh look at the foundational problems in this context, is the advent of multiple gravitational models in which Lorentz symmetry is only emergent. In this setting, I propose a new understanding of records as certain relations between two configurations, the recorded one and the record-holding one. These relations are formalized through  a factorization of the amplitude kernel, which forbids unwanted 'recoherence' of branches. On this basis, I show that in simple cases the Born rule is consistent with counting the relative density of observers with the same records. Furthermore, unlike what occurs in consistent histories,  in this context there is indeed a preferred notion of coarse-grainings: those centered around piece-wise classical paths in configuration space (with a certain radius).  Thus, this new understanding  claims to resolve aspects of the measurement problem which are still deemed controversial in the standard approaches (but which probably leaves others open...).

In this talk we will discuss the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model. Finally, we discuss applications of these results to problems in joint mesurability, and for EPR steering using randomly chosen measurements.

To best distinguish between classical and non-classical models of nature requires a good notion of classicality. I will argue that noncontextuality is a good candidate for this notion. Until now, certain theoretical and experimental roadblocks have stood in the way of a test of noncontextuality which is free of unattainable experimental idealizations. I will present solutions to these roadblocks as well as the results of an experimental test.

One necessity to avoid the measurement problem in quantum mechanics is a clear ontology. Such an ontology is for instance provided by Bohmian mechanics. In the non-relativistic regime, Bohmian mechanics is a theory about particles whose motion is governed by a velocity field. The latter is generated by a wave

function solving the Schrödinger equation. In view of Feynman's criticism towards classical field theory one may wonder whether such a complex object as the wave function is needed to account for quantum phenomena. After all the value of the velocity field, i.e., of the wave function, is only needed in the vicinity of the configuration of the particle positions, however, it is defined everywhere in configuration space, even in places where the configuration might never roam.  In a joint work with M. Hall and H. Wiseman we were able to formulate an approach to quantum mechanics that is capable to describe typical quantum phenomena like interference without a wave function, having only particles.  This approach comes at the cost of introducing many classical worlds, hence the name Many-Interacting-Worlds approach (MIW). In MIW the force on each particle is given by 1) Newton's force describing the interaction within each world and 2) an additional force term describing an interaction between the worlds.  Similar approaches have been suggested by B. Poirier and C. Sebens. I will give an overview on MIW, discuss the nature of its equations of motion, and its empirical import.