Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Martingale Models for Quantum State Reduction   Stochastic models for quantum state reduction give rise to statistical laws
that are in most respects in agreement with those of quantum measurement
theory. Here we examine the correspondence of the two theories in detail,
making a systematic use of the methods of martingale theory. An analysis is
carried out to determine the magnitude of the fluctuations experienced by the
expectation of the observable during the course of the reduction process and an
upper bound is established for the ensemble average of the greatest
fluctuations incurred. We consider the general projection postulate of L\"uders
applicable in the case of a possibly degenerate eigenvalue spectrum, and derive
this result rigorously from the underlying stochastic dynamics for state
reduction in the case of both a pure and a mixed initial state. We also analyse
the associated Lindblad equation for the evolution of the density matrix, and
obtain an exact time-dependent solution for the state reduction that explicitly
exhibits the transition from a general initial density matrix to the L\"uders
density matrix. Finally, we apply Girsanov's theorem to derive a set of simple
formulae for the dynamics of the state in terms of a family of geometric
Brownian motions, thereby constructing an explicit unravelling of the Lindblad
equation.

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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga