106 research outputs found
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
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
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
Quantum retrodiction: foundations and controversies
Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum retrodiction and highlight its intimate connection with the Bayesian interpretation of probability. The close link with Bayesian methods enables us to explore controversies and misunderstandings about retrodiction that have appeared in the literature. To be clear, quantum retrodiction is universally applicable and draws its validity directly from conventional predictive quantum theory coupled with Bayes’ theorem
- …