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Random quantum states are useful in various areas of quantum informationscience. Distributions of random quantum states using Gaussian distributionshave been used in various scenarios in quantum information science. One of thisis the distribution of random quantum states derived using the Wishartdistibution usually used in statistics. This distribution of random quantumstates using the Wishart distribution has recently been named as the quantumWishart distribution \cite{Han}. The quantum Wishart distribution has beenfound for non-central distribution with a general covariance matrix and zeromean matrix. Here, we find out the closed form expression for the distributionof random quantum states pertaining to non-central Wishart distribution withany general rank one mean matrix and a general covariance matrix for arbitrarydimensions in both real and complex Hilbert space. We term this as the non-zeromean quantum Wishart distribution. We find out the method for the desiredplacement of its peak position in the real and complex Hilbert space forarbitrary dimensions. We also show an application of this via a fast andefficient algorithm for the random sampling of quantum states, mainly forqubits where the target distribution is a well behaved arbitrary probabilitydistribution function occurring in the context of quantum state estimationexperimental data .

Non-Zero Mean Quantum Wishart Distribution Of Random Quantum States And Application