Quantum measurement theory

Günther Ludwig

No measurement is possible without any theory. With respect to a theory under consideration one has to distinguish between direct and indirect measurements. Direct measurements are defined by pre-theories, i.e. without the theory under consideration. The direct measurements for quantum theory are given by measurable processes on macroscopic devices. It is demonstrated how indirect measurements in quantum mechanics can be reduced to direct measurements. A theory of the measuring device is in this context not possible by quantum mechanics alone, but by a more comprehensive theory of macrosystems.

János A. Bergou, Mark S. Hillery, Mark E. Saffman

Kazuya Okamura

In this study, we develop quantum measurement theory for quantum systems described by C∗-algebras. This is the first step to establish measurement theory for interacting quantum fields with off-shell momenta. Unlike quantum mechanics (i.e., quantum systems with finite degrees of freedom), measurement theory for quantum fields is still in development because of the difficulty of quantum fields that are typical quantum systems with infinite degrees of freedom. Furthermore, the mathematical theory of quantum measurement is formulated in the von Neumann algebraic setting in previous studies. In the paper, we aim to extend the applicable area of quantum measurement theory to quantum systems described by C∗-algebras from a mathematical viewpoint, referring to the sector theory that is related to symmetry and based on the theory of integral decomposition of states. In particular, we define central subspaces of the dual space of a C∗-algebra and use them to define instruments. This attempt makes the connection between measurement theory and sector theory explicit and enables us to understand the macroscopic nature and the physical meaning of measurement.

János A. Bergou, Mark S. Hillery

Morgan, Peter

Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce noncommutativity into classical measurement theory, we can also add quantum noise, differentiated from thermal noise by Poincaré invariance. With these two changes, the extended classical and quantum measurement theories are equally capable, so we may speak of a single "measurement theory". The reconciliation of general relativity and quantum theory has been long delayed because classical and quantum systems have been thought to be very different, however this unification allows us to discuss a unified measurement theory for geometry in physics.

Jan Peřina, Z. Hradil, Branislav Jurčo