  Random quantum states are useful in various areas of quantum information
science. Distributions of random quantum states using Gaussian distributions
have been used in various scenarios in quantum information science. One of this
is the distribution of random quantum states derived using the Wishart
distibution usually used in statistics. This distribution of random quantum
states using the Wishart distribution has recently been named as the quantum
Wishart distribution \cite{Han}. The quantum Wishart distribution has been
found for non-central distribution with a general covariance matrix and zero
mean matrix. Here, we find out the closed form expression for the distribution
of random quantum states pertaining to non-central Wishart distribution with
any general rank one mean matrix and a general covariance matrix for arbitrary
dimensions in both real and complex Hilbert space. We term this as the non-zero
mean quantum Wishart distribution. We find out the method for the desired
placement of its peak position in the real and complex Hilbert space for
arbitrary dimensions. We also show an application of this via a fast and
efficient algorithm for the random sampling of quantum states, mainly for
qubits where the target distribution is a well behaved arbitrary probability
distribution function occurring in the context of quantum state estimation
experimental data .
