On the structure of covariant phase observables

We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W*-algebra with phase matrices as its subset. The properties of the Radon-Nikodym derivatives of phase probability measures are studied.Comment: 11 page

The Pegg-Barnett Formalism and Covariant Phase Observables

We compare the Pegg-Barnett (PB) formalism with the covariant phase observable approach to the problem of quantum phase and show that PB-formalism gives essentially the same results as the canonical (covariant) phase observable. We also show that PB-formalism can be extended to cover all covariant phase observables including the covariant phase observable arising from the angle margin of the Husimi Q-function.Comment: 10 page

Extreme phase and rotated quadrature measurements

We determine the extreme points of the convex set of covariant phase observables. Such extremals describe the best phase parameter measurements of laser light - the best in the sense that they are free from classical randomness due to fluctuations in the measuring procedure. We also characterize extreme fuzzy rotated quadratures

Weak vs. approximate values in quantum state determination

We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory of sequential measurements. We then present a detailed analysis of the recent experiment of Lundeen et al. concerning the reconstruction of the state of a photon using weak measurements. We compare their method with the reconstruction method through informationally complete phase space measurements and show that it lacks the generality of the phase space method. In particular, a completely unknown state can never be reconstructed using the method of weak measurements.Comment: 6 page

On the complementarity of the quadrature observables

In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon tranform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.Comment: Dedicated to Peter Mittelstaedt in honour of his eightieth birthda

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

A single dose of mirtazapine attenuates neural responses to self-referential processing

Increased self-focus is a core factor in the psychopathology of depression. Cortical midline structures (CMS) are implicated in the neurobiology of self, depression and antidepressant treatment response. Mirtazapine, an antidepressant that increases serotonin and norepinephrine release, enhances processing of positive and attenuates processing of negative emotional information in healthy volunteers after a single dose. These early changes, which are opposite to the negative information bias in depression, may be important for the therapeutic effect of mirtazapine. It nevertheless remains unresolved whether/how mirtazapine specifically influences processing of self-referential emotional information. Half of the healthy volunteers (n=15/30) received a single dose of mirtazapine, in an open-label design, two hours before functional magnetic resonance imaging (fMRI), and the other half was scanned as a control group without medication. During fMRI the participants categorized positive and negative self-referential adjectives. Mirtazapine attenuated responses to self-referential processing in the medial prefrontal cortex and the anterior cingulate cortex. Mirtazapine further decreased responses to positive self-referential processing in the posterior cingulate cortex and parietal cortex. These decreased responses of the CMS suggest that mirtazapine may rapidly improve the ability of the CMS to down-regulate self-referential processing. In depressed patients, this could lead to decreased self-focus and rumination, contributing to the antidepressant effect.Peer reviewe