This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
Anomalies are a ubiquitous phenomenon in quantum mechanics whereby a classical
symmetry is irrevocably violated by quantization. Anomalies not only constrain the
space of classical theories than are consistent with quantum mechanics but are
responsible for rich, surprising and experimentally tested physical phenomena.
In this talk I will give a non-technical, bird's eye introduction to anomalies.
Seminal work of Steve Lack showed that universal algebraic theories (PROPs) may be composed to produce more sophisticated theories. I’ll apply this method to construct an axiomatic version of the theory of a pair of complementary observables starting from the theory of monoids. How far can we get with this? Quite far! We’ll get a large chunk of finite dimensional quantum theory this way —but the fact that quantum systems have non-trivial dynamics means that it’s (always) possible to present the resulting theory as a composite PROP in Lack’s sense. If time permits, I’ll also discuss how
Analyzing characteristics of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. For example, device-independence is a very important feature in the study of quantum cryptography where the quantum devices may not be trusted. In this talk, I will discuss the ability to characterize the state that Alice and Bob share in various physical scenarios using only the correlation data.
A geometric approach to investigation of quantum entanglement is advocated.
We discuss first the geometry of the (N^2-1)--dimensional convex body
of mixed quantum states acting on an N--dimensional Hilbert space
and study projections of this set into 2- and 3-dimensional spaces.
For composed dimensions, N=K^2, one consideres the subset
of separable states and shows that it has a positive measure.
Analyzing its properties contributes to our understanding of
quantum entanglement and its time evolution.
To describe observed phenomena in the lab and to apply superposition principle to gravity, quantum theory needs to be generalized to incorporate indefinite causal structure. Practically, indefinite causal structure offers advantage in communication and computation. Fundamentally, superposing causal structure is one approach to quantize gravity (spacetime metric is equivalent to causal structure plus conformal factor, so quantizing causal structure effectively quantizes gravity).
The on-demand generation of bright entangled photon pairs is highly needed in quantum optics and emerging quantum information applications. However, a quantum light source combining both high fidelity and on-demand bright emission has proven elusive with current leading photon technologies. In this work we present a new bright nanoscale source of strongly entangled photon pairs generated with a position controlled nanowire quantum dot. The major breakthrough in the nanowire growth to achieve both bright photon emission and highly entangled photon pairs will be discussed [2, 3].
In this talk I will review the construction of space starting purely from quantum mechanics and without assuming that the notion of space is attached to a preconceived notion of classical reality. I will show that if one start with the simplest notion of a quantum system encoded into the Heisenberg group algebra one naturally obtain a notion of space that generalizes the usual notion of Euclidean space.
Can we decompose the information of a composite system into terms arising from its parts and their interactions?
For a bipartite system (X,Y), the joint entropy can be written as an algebraic sum of three terms: the entropy of X alone, the entropy of Y alone, and the mutual information of X and Y, which comes with an opposite sign. This suggests a set-theoretical analogy: mutual information is a sort of "intersection", and joint entropy is a sort of "union".
In order to solve the problem of quantum gravity, we first need to pose the problem. In this talk I will argue that the problem of quantum gravity arises already in the domain of quantum mechanics and the relativity principle. Specifically, the relativity principle implies that the concept of inertial motion should extend also to those systems that are in quantum superpositions of inertial motions. By contrast, relativistic quantum field theory only considers the point of view of classical observers in states of definite relative motion (i.e.