Positive Operator Value Measures on Hilbert Spaces

A positive operator value measure (POVM) on a separable Hilbert space is defined [2,5 ] to be any sequence of operators on such that for each , is positive and

In this paper, we use frames to show the existence of positive operator value measure on a separable Hilbert space and vice versa. Also using frames we shall discuss the average probability of an incorrect quantum measurement. Finally, we relate frames with projective valued measurements.

References

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2. E. Desurvire, Classical and Quantum Information Theory, Cambridge

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4. M. Hayashi, Quantum Information, Springer Berlin Heidelberg, New York, 2006.

5. Mark M. Wilde, Quantum Information Theory, Cambridge University Press, 2013.