Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

Extinction times for a general birth, death and catastrophe process

The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.

Effectiveness of a mutual support group for families of patients with schizophrenia

Aim. This paper reports a study to examine the effectiveness of a 12-session mutual support group for Chinese families caring for a relative with schizophrenia compared with a psycho-educational group and routine family support services in Hong Kong. Background. Schizophrenia is a disruptive and distressing illness for patients and their families. With the current trend of community care for mental illness, there is evidence that family intervention reduces patient relapse and re-hospitalization, satisfies the health needs of families and enhances their coping capabilities. Methods. A randomized controlled trial was conducted from May 2002 to June 2003 with 96 Chinese families of a relative with schizophrenia selected from two psychiatric outpatient clinics in Hong Kong. Families were randomly assigned to receive mutual support (n = 32), psycho-education (n = 33) or standard care only (n = 31). The interventions were delivered at outpatient clinics over a 6-month period. Pre- and post- (1 week and 6 months) testing took place and families' functioning, mental health service utilization, patients' level of functioning and duration of re-hospitalization were measured. Results. At both post-test periods, family caregivers and patients in the mutual support group reported statistically significant improvements on family and patients' level of functioning, when compared with their counterparts in the psycho-education and standard care groups. Conclusions. The findings support the use of mutual support groups as an effective modality of family intervention in a Chinese population caring for a family member with schizophrenia to improve both family and patient functioning.

Measuring nonlinear functionals of quantum harmonic oscillator states

Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and nonlinear functionals of an arbitrary oscillator state. This leads to many applications including purity tests, eigenvalue estimation, entropy, and distance measures-all without the need for nonlinear interactions or complete state reconstruction. Remarkably, experimental realization of the proposed scheme is already within the reach of current technology with linear optics.