Quantum retrodiction in open systems

Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum mechanics. Recent interest in quantum communications and cryptography, however, has provided retrodiction with a potential practical application. For this purpose quantum retrodiction in open systems should be more relevant than in closed systems isolated from the environment. In this paper we study retrodiction in open systems and develop a general master equation for the backward time evolution of the measured state, which can be used for calculating preparation probabilities. We solve the master equation, by way of example, for the driven two-level atom coupled to the electromagnetic field.Comment: 12 pages, no figure

Retrodictive states and two-photon quantum imaging

We use retrodictive quantum theory to analyse two-photon quantum imaging systems. The formalism is particularly suitable for calculating conditional probability distributions.Comment: 5 pages, 3 figure

Retrodiction as a tool for micromaser field measurements

We use retrodictive quantum theory to describe cavity field measurements by successive atomic detections in the micromaser. We calculate the state of the micromaser cavity field prior to detection of sequences of atoms in either the excited or ground state, for atoms that are initially prepared in the excited state. This provides the POM elements, which describe such sequences of measurements.Comment: 20 pages, 4(8) figure

The rich get richer: patterns of plant invasions in the United States

Observations from islands, small-scale experiments, and mathematical models have generally supported the paradigm that habitats of low plant diversity are more vulnerable to plant invasions than areas of high plant diversity. We summarize two independent data sets to show exactly the opposite pattern at multiple spatial scales. More significant, and alarming, is that hotspots of native plant diversity have been far more heavily invaded than areas of low plant diversity in most parts of the United States when considered at larger spatial scales. Our findings suggest that we cannot expect such hotspots to repel invasions, and that the threat of invasion is significant and predictably greatest in these areas

Quantum theory of preparation and measurement

The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric postulate is presented, from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. It is shown that the new postulate is perfectly consistent with the conventional postulate.Comment: 25 pages, No figure

Measurement master equation

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated quantum trajectories we find Rabi oscillations, Zeno-effect type behaviour and random telegraph evolution spawned by mini quantum jumps as we change the rates and strengths of measurement.Comment: 14 pages and 8 figures, Optics Communications in pres

Quantum probability rule : a generalization of the theorems of Gleason and Busch

Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory

Point source generation of chiral fields:measures of near- and far-field optical helicity

To consider the relationship between different measures of chirality in an optical field, the simplest case is considered: direct spontaneous emission of circularly polarized light by a point source. In the electromagnetic fields radiated from a suitably chiral source, such as a low-symmetry chiral molecule undergoing radiative decay, optical helicity is exhibited in the extent of a difference in left- and right-handed circular polarization components. There are several practical measures for quantifying the emergence of ensuing optical helicity, exhibiting different forms of dependence on the properties of the emitter and the positioning of a detector. By casting each measure in terms of an irreducible helicity density, connections and distinctions can be drawn between results expressible in either classical or quantum form