  The fluctuations of electrical current provide information on the dynamics of
electrons in quantum devices. Understanding the nature of these fluctuations in
a quantum dot is thus a crucial step insofar as this system is the elementary
brick of quantum circuits. In this context, we develop a theory for calculating
the quantum noise at finite frequency in a quantum dot connected to two
reservoirs in the presence of interactions and for any symmetry of the
couplings to the reservoirs. This theory is developed in the framework of the
Keldysh non-equilibrium Green function technique. We establish an analytical
expression for the quantum noise in terms of the various transmission
amplitudes between the reservoirs and of some effective transmission
coefficient which we define. We then study the noise as a function of the dot
energy level and the bias voltage. The effects of both Coulomb interactions in
the dot and asymmetric couplings with the reservoirs are characterized.
