Measurement-Based Quantum Foundations

John L. McKnight

James L Park

János A. Bergou, Mark S. Hillery

Masanao Ozawa

The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement theory based on completely positive map-valued measures, a universally valid new formulation of the uncertainty principle for error and disturbance in quantum measurements, the Wigner-Araki-Yanase limit of quantum measurements, the accuracy limit of quantum computing based on conservation laws, and a quantum interpretation based on quantum set theory.

Howard M. Wiseman, Gerard J Milburn

Gregg S. Jaeger

The notion of macroscopic realism has been used in attempts to achieve consistency between physics and everyday experience and to locate some boundary between the realms of classical mechanics and quantum meachanics. Its ostensibly underlying conceptual components, realism and macroscopicity, have most often appeared in the foundations of physics in relation to quantum measurement: reality became a prominent topic of discussion in quantum physics after the notion of element of reality was defined and used by Einstein, Podolsky and Rosen in that context, and macroscopicity is often explicitly assumed to be an essential property of any measuring apparatus. However, macroscopicity turns out to be a rather vaguer and less consistently understood notion than typically assumed by physicists who have not explicitly explored the notion themselves. For this reason, it behooves those investigating the foundations of quantum mechanics from a realist perspective to look for alternative notions for grounding quantum measurement. Here, the merits of treating the measuring instrument as a ‘natural kind’ as a means of avoiding anthropocentrism in the foundations of quantum measurement are pointed out as a means of advancing quantum measurement theory.