Talks

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.

Inspired by quantum information approaches to thermodynamics, we introduce a general framework for resource theories, from the perspective of subjective agents. First we formalize a way to think of subjective knowledge through what we call specification spaces, where states of knowledge (or specifications) are represented by sets whose elements are the possible states of reality admitted by an observer. We explore how to conciliate different views of reality via embeddings between specification spaces. Then we introduce resource theories on specification spaces, which are constructed from a set of allowed operations, imposing a pre-order structure in the specification space. We see how to relate, combine and create different resource theories. The local structure of a specification space (which in quantum theory is given by tensoring different Hilbert spaces) is not assumed a priori. Instead, we derive it operationally from commutativity relations in the set of transformations. Further applications are discussed.

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.