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

   University Press, New York, 2009.

    

3. Y. C. Eldar and G. D. Forney, Optimal Tight Frames and Quantum Measurement, IEEE Transactions on Information Theory, Vol. 48(3), 599-610.

    

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

    

    

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