Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schrö dinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions. [S0034-6861(98)00601-1] CONTENTS

We address the joint estimation of the two defining parameters of a displacement operation in phase space. In a measurement scheme based on a Gaussian probe field and two homodyne detectors, it is shown that both conjugated parameters can be measured below the standard quantum limit when the probe field is entangled. We derive the most informative Cram\'er-Rao bound, providing the theoretical benchmark on the estimation and observe that our scheme is nearly optimal for a wide parameter range characterizing the probe field. We discuss the role of the entanglement as well as the relation between our measurement strategy and the generalized uncertainty relations.Comment: 8 pages, 3 figures; v2: references added and sections added to the supplemental material; v3: minor changes (published version

There was a minor error in the published version of our Letter, which does not change the conclusions. In Eqs. (5) and (6) of the published version, V n11 should be replaced by V n throughout. The matrix r n af , just prior to Eq. (6), should be replaced byAll of the above changes result in the interchange of C and S in Eq. (8) of the published version with the new expression for L n given byThe plot of L n with t then changes slightly and is redrawn in this Erratum as Fig. 1.From the new Fig. 1, it is clear that corresponding to a projection onto the j0͘, j1͘ subspace, the atom-cavity state is now always entangled except for values of t np͞2. Compared with the earlier version of the Letter, this is a much larger domain for t, for which the state remains entangled. Thus, our conclusions about the presence of entanglement are strengthened. 0 1 2 3 4 5 6 7 8 9 1 0 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 Λ n t FIG. 1. Plots of the time variation of the inseparability expression L for three values of n. The fastest oscillating curve is for n 100, the next fastest for n 10, and the slowest oscillating curve is for n 0.

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