Constructing Operator Valued Probability Measures in Phase Space

Details Constructing Operator Valued Probability Measures in Phase Space Constructing Operator Valued Probability Measures in Phase Space

2006-11-28

arxiv.org/abs/quant-ph/0611278v1

Physics

Quantum Physics

6pages, no figures, to appear in Proceedings of Foundations of Probability and Physics, held at Vaxjo University, Sweden, June

Scientific paper

Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are investigated in terms of geometric positive trace increasing maps (PTI), for general 1D domains, as well as 2D shapes e.g. circles, disks. Spectral properties of OVMs and operational implementations of their constructing PITs are discussed.

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