**An almost convincing scheme for discrimination of preparation basis for a quantum ensemble and why it will not work**

Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture
of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. The
non-unique decomposition of a density matrix makes it impossible to estimate the preparation basis for the quantum
system. Here we present a measurement scheme to (seemingly) improve the performance of unsharp measurements.
We argue that in some situations this scheme is capable of providing statistics from a single quantum system, thus,
making it possible to perform state tomography from a single copy. One of the byproduct of the scheme is a way
to distinguish between different preparation methods used to prepare the state of the quantum system. However, our
numerical simulations disagree with our intuitive predictions. We show that a counter-intuitive property of biased
classical random walk is responsible for the proposed mechanism to not work.