  The capacity of a discrete-time multiple-input-multiple-output channel with
correlated phase noises is investigated. In particular, the electro-optic
frequency comb system is considered, where the phase noise of each channel is a
combination of two independent Wiener phase-noise sources. Capacity upper and
lower bounds are derived for this channel and are compared with lower bounds
obtained by numerically evaluating the achievable information rates using
quadrature amplitude modulation constellations. Capacity upper and lower bounds
are provided for the high signal-to-noise ratio (SNR) regime. The multiplexing
gain (pre-log) is shown to be $M-1$, where $M$ represents the number of
channels. A constant gap between the asymptotic upper and lower bounds is
observed, which depends on the number of channels $M$. For the specific case of
$M=2$, capacity is characterized up to a term that vanishes as the SNR grows
large.
