Quantum Physics

All known hidden variable theories that completely reproduce all quantum predictions share the feature that they add some information to the quantum state "psi". That is, if one knew the "state of reality" given by the hidden variable(s) "lambda", then one could infer the quantum state - the hidden variables are additional to the quantum state. However, for the case of a single 2-dimensional quantum system Kochen and Specker gave a model which does not have this feature – the non-orthogonality of two quantum states is manifested as overlapping probability distributions on the hidden variables, and teh model could be termed “psi-epistemic”. A natural question arises whether a similar model is possible for higher dimensional systems. At the time of writing this abstract I have no clue. I will talk about various constraints on such theories (in particular on how they manifest contextuality) and I'll present some examples of failed attempts to construct such models for a 3-dimensional system. I will also discuss a very artificial tweaking of Bell’s original hidden variable model which renders it psi-epistemic for some (though not all) of the corresponding quantum states.

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. But what happens if one drops (b), or (a), or both, as some have been inclined to? Can one achieve a consistent view then? A major worry is illustrated by the Wigner's friend scenario: it looks as if it should make a measurable difference where one puts the cut, so how can it be consistent to slide it around (as, e.g., Bohr was wont to)? I'll discuss two main cases: that of Asher Peres' book, which adopts (a) but drops (b); and that of the quantum Bayesians Caves, Fuchs and Shack, which drops both. A view of Peres' sort can I, think, be made consistent, though may look a little strained; the quantum Bayesians' can too, though there are some subtleties (which I shall discuss) about how one should handle Wigner's friend.

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. [1] Lev S Bishop et al 2009 New J. Phys. 11 073040

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. We exhibit four independent reasons for not giving into this temptation. A more likely possibility is that it can play the role of ``dark matter''. Indeed, as noted in scale invariance seems to play a role in the MOND phenomenology. Spatial boundary conditions are derived from the free-endpoint variation method and a preliminary analysis of the constraints and their propagation in the Hamiltonian formulation is presented.

At NIST we are engaged in an experiment whose goal is to create superpositions of optical coherent states (such superpositions are sometimes called "Schroedinger cat" states). We use homodyne detection to measure the light, and we apply maximum likelihood quantum state tomography to the homodyne data to estimate the state that we have created. To assist in this analysis we have made a few improvements to quantum state tomography: we have devised a new iterative method (that has faster convergence than R*\rho*R iterations) to find the maximum likelihood state, we have formulated a stopping criterion that can upper-bound the actual maximum likelihood, and we have implemented a bias-corrected resampling strategy to estimate confidence intervals.