Thursday, June 6, 2013

1306.0349 (G. Sentís et al.)

Decomposition of any quantum measurement into extremals    [PDF]

G. Sentís, B. Gendra, S. D. Bartlett, A. C. Doherty
We design an efficient and constructive algorithm to decompose any generalized quantum measurement into a convex combination of extremal measurements. We show that if one allows for a classical post-processing step only extremal rank-1 POVMs are needed. For a measurement with $N$ elements on a $d$-dimensional space, our algorithm will decompose it into at most $(N-1)d+1$ extremals, whereas the best previously known upper bound scaled as $d^2$. Since the decomposition is not unique, we show how to tailor our algorithm to provide particular types of decompositions that exhibit some desired property.
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