This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
I will give an overview of two ways to estimate parameters with a quantum system when the dynamics is nontrivial. In the first case, the parameter is changing in an irregular way, and we use consider the use of continuous measurement to track it in time. Tracking speed is of the essence for feedback purposes, and I will present our new and improved way to speed up the estimation algorithm. In the second case, I will consider the use of Hamiltonian control to estimate a fixed parameter, but of a time-dependent Hamiltonian.
Throughout the development of quantum mechanics, the striking refusal of nature to obey classical reasoning and intuition has driven both curiosity and confusion. From the apparent inescapably probabilistic nature of the theory, to more subtle issues such as entanglement, nonlocality, and contextuality, it has always been the `nonclassical’ features that present the most interesting puzzle. More recently, it has become apparent that these features are also the primary resource for quantum information processing.
We investigate the quantum trajectories of jointly monitored transmon qubits, tracking measurement-induced entanglement creation as a continuous process. The quantum trajectories naturally split into low and high entanglement classes corresponding to partial parity collapse. We theoretically calculate the distribution of concurrence at any given time and show good agreement with the constructed histogram of measured concurrence trajectories. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary.
In the device-independent paradigm, the labeling of parties/inputs/outputs has no physical meaning and thus the behavior of the system should be studied up to symmetry. We conduct the first formal study of relabelings appearing in Bell scenarios. The talk includes a review of previous works, a definition of Bell relabeling groups illustrated by examples, and applications, including the classification of Bell inequalities, the generalization of binary correlators to d outcomes and the computation of exact bounds using the NPA hierarchy.
In this talk I would like to put forward Wasserstein-geometry as a natural language for Quantum hydrodynamics. Wasserstein-geometry is a formal, infinite dimensional, Riemannian manifold structure on the space of probability measures on a given Riemannian manifold. The basic equations of Quantum hydrodynamics on the other hand are given by the Madelung equations. In terms of Wasserstein-geometry, Madelung equations appear in the shape of Newton's second law of motion, in which the geodesics are disturbed by the influence of a quantum potential.
In quantum theory every state can be diagonalised, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This fact is crucial in quantum statistical mechanics, as it provides the foundation for the notions of majorisation and entropy. A natural question then arises: can we give an operational characterisation of them? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that every state can be diagonalised: Causality, Purity Preservation, Purification, and Pure Sharpness.
Recent findings on quantitative growth patterns have revealed striking generalities across the tree of life, and recurring over distinct levels of organization. Growth-mass relationships in 1) individual growth to maturity, 2) population reproduction, 3) insect colony enlargement and 4) community production across wholeecosystems of very different types, often follow highly robust near ¾ scaling laws. These patterns represent some of the most general relations in biology, but the reasons they are so strangely similar across levels of organization remains a mystery.
As discussed in last week’s colloquium, the use of the p-adic metric in state space provides a route to resolving the Bell Theorem in favour of realism and local causality, without fine tuning. Here the p-adic integers provide a natural way to describe the fractal geometry of Invariant Set Theory’s state space. In this talk I first explore the role of complex numbers in Invariant Set Theory (arXiv:1605.01051), and describe a novel realistic perspective on quantum interferometry.