A New Relation between post and pre-optimal measurement states

Details A New Relation between post and pre-optimal measurement states A New Relation between post and pre-optimal measurement states

2004-06-23

arxiv.org/abs/quant-ph/0406169v1

Phys.Rev. A72 024102(2005)

Physics

Quantum Physics

4 pages in REVTEX

Scientific paper

10.1103/PhysRevA.72.024102

When an optimal measurement is made on a qubit and what we call an Unbiased Mixture of the resulting ensembles is taken, then the post measurement density matrix is shown to be related to the pre-measurement density matrix through a simple and linear relation. It is shown that such a relation holds only when the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is also shown explicitly that non-orthogonal measurements fail to give such a linear relation no matter how the ensembles are mixed. The result has been proved to be true for arbitrary quantum mechanical systems of finite dimensional Hilbert spaces. The result is true irrespective of whether the initial state is pure or mixed.

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