Fundamentals of measurement theory

Matthias Kleinmann, Tamás Vértesi, Adán Cabello

Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we show that fundamentally binary theories are experimentally testable with current technology. For that, we identify a feasible Bell-type experiment on pairs of entangled qutrits. In addition, we prove that, for any $n$, quantum $n$-ary correlations are not fundamentally $(n\ensuremath{-}1)$-ary. For that, we introduce a family of inequalities that hold for fundamentally $(n\ensuremath{-}1)$-ary theories but are violated by quantum $n$-ary correlations.

Roger Balian

Gerben J. Stavenga

The fundamental aspect of measurement, that a measurement always results in a record, is analysed. Recording implies irreversibility and entropy production in the combined system of instrument and object. In elementary particle physics the record itself is all important, and therefore the entropy production due to measurement, hitherto neglected in fundamental theories, is essential. The conjecture is advanced that, just as in relativity the signal is of prime importance and in quantum theory the measuring interaction is fundamental, this (third) aspect of measurement will play a central role in a new fundamental theory of elementary particles. Some basic notions of this new theory are proposed. The stable particle, for example, can be conceived of as a steady state of an open system, characterized by minimal entropy production. Finally the meaning of irreversibility on the micro-level of elementary particles is discussed.

Paul Busch, PEKKA J. LAHTI

Akira Shimizu

Quantum information theory is closely related to quantum measurement theory because one must perform measurement to obtain information on a quantum system. Among many possible limits of quantum measurement, the simplest ones were derived directly from the uncertainty principles. However, such simple limits are not the only limits. I here suggest a new limit which comes from the forms and the strengths of the elementary interactions. Namely, there are only four types of elementary interactions in nature; their forms are determined by the gauge invariance (and symmetry breaking), and their coupling constants (in the low-energy regime) have definite values. I point out that this leads to a new fundamental limit of quantum measurements. Furthermore, this fundamental limit imposes the fundamental limits of getting information on, preparing, and controlling quantum systems.

Henry Krips