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arXiv · 1306.0349

Decomposition of any quantum measurement into extremals

G. Sentís·B. Gendra·S. D. Bartlett·A. C. Doherty
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Abstract

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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G. Sentís, B. Gendra, S. D. Bartlett, A. C. Doherty. 2013-06-03. Decomposition of any quantum measurement into extremals. https://doi.org/10.1088/1751-8113/46/37/375302

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