  This paper extends the Karhunen-Loeve representation from classical Gaussian
random processes to quantum Wiener processes which model external bosonic
fields for open quantum systems. The resulting expansion of the quantum Wiener
process in the vacuum state is organised as a series of sinusoidal functions on
a bounded time interval with statistically independent coefficients consisting
of noncommuting position and momentum operators in a Gaussian quantum state. A
similar representation is obtained for the solution of a linear quantum
stochastic differential equation which governs the system variables of an open
quantum harmonic oscillator. This expansion is applied to computing a
quadratic-exponential functional arising as a performance criterion in the
framework of risk-sensitive control for this class of open quantum systems.
