This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of physical reality that both serve to describe.
The discovery of postquantum nonlocality, i.e. the existence of nonlocal correlations stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers.
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.
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.
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.
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.
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.
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.
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.