This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
In this talk I will report on a recent work [arXiv:0908.1583], which investigates general probabilistic theories where every mixed state has a purification, unique up to reversible channels on the purifying system. The purification principle is equivalent to the existence of a reversible realization for every physical process, namely that to the fact that every physical process can be regarded as arising from the reversible interaction of the input system with an environment that is eventually discarded.
CMB measurements reveal a very smooth early universe. We propose a mech- anism to make this smoothness natural by weakening the strength of gravity at early times, and therefore altering which initial conditions have low entropy.
For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure.
In his brilliant article "Against 'Measurement'", John Bell famously
argued that the word has had such a damaging effect on the discussion,
that it should now be banned altogether in quantum mechanics. But in
the beginning was the word, and the word is still with us. Indeed,
David Mermin responded In Praise of Measurement that within the field
of quantum computer science the concept of measurement is precisely
defined, unproblematic, and forms the foundation of the entire
subject, a verdict reaffirmed by the development of measurement-based
A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.
Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of the probability calculus and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that an agent’s degrees of belief be coherent.
Instrumentalism about the quantum state is the view that this mathematical object does not serve to represent a component of (non-directly observable) reality, but is rather a device solely for making predictions about the results of experiments. One honest way to be such an instrumentalist is a) to take an ensemble view (= frequentism about quantum probabilities), whereby the state represents predictions for measurement results on ensembles of systems, but not individual systems and b) to assign some specific level for the quantum/classical cut.
I will present recent work [1] on preparation by measurement of Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. In particular, for the 3-qubit case, when employing a nonlinear filter on the recorded homodyne signal the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions. I will discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.
We present a first-principles implementation of {\em spatial} scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching. In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential A_k as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious, but physically questionable, theory, the equations of motion of this new theory are second order in time-derivatives. It is tempting to try to interpret the vector potential A_k as the electromagnetic field.
Betting (or gambling) is a useful tool for studying decision-making in the face of [classical] uncertainty. We would like to understand how a quantum "agent" would act when faced with uncertainty about its [quantum] environment. I will present a preliminary construction of a theory of quantum gambling, motivated by roulette and quantum optics. I'll begin by reviewing classical gambling and the Kelly Criterion for optimal betting. Then I'll demonstrate a quantum optical version of roulette, and discuss some of the challenges and pitfalls in designing such analogues.