Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

What Price Recreation in Finland?—A Contingent Valuation Study of Non-Market Benefits of Public Outdoor Recreation Areas

Basic services in Finnish national parks and state-owned recreation areas have traditionally been publicly financed and thus free of charge for users. Since the benefits of public recreation are not captured by market demand, government spending on recreation services must be motivated in some other way. Here, we elicit people’s willingness to pay (WTP) for services in the country’s state-owned parks to obtain an estimate of the value of outdoor recreation in monetary terms. A variant of the Tobit model is used in the econometric analysis to examine the WTP responses elicited by a payment card format. We also study who the current users of recreation services are in order to enable policymakers to anticipate the redistribution effects of a potential implementation of user fees. Finally, we discuss the motives for WTP, which reveal concerns such as equity and ability to pay that are relevant for planning public recreation in general and for the introduction of fees in particular