On the completeness of quantum theory

Arthur I. Fine

Zeng‐Bing Chen

Quantum mechanics is a cornerstone of our current understanding of nature and extremely successful in describing physics covering a huge range of scales. However, its interpretation remains controversial since the early days of quantum mechanics. What does a quantum state really mean? Is there any way out of the so-called quantum measurement problem? Here, we present an information-complete quantum theory (ICQT) and the trinary property of nature to beat the above problems. We assume that a quantum system’s state provides an information-complete description of the system in the trinary picture. We present a consistent formalism of quantum theory that makes the information-completeness explicitly and argue that conventional quantum mechanics is an approximation of the ICQT. We then show how our ICQT provides a coherent picture and fresh angle of some existing problems in physics. The computational content of our theory is uncovered by defining an information-complete quantum computer.

Tim Maudlin

In 1935, Einstein, Podolsky and Rosen raised the issue of the completeness of the quantum description of a physical system. What they had in mind is whether or not the quantum description is informationally complete, in that all physical features of a system can be recovered from it. In a collapse theory such as the theory of Ghirardi, Rimini and Weber, the quantum wavefunction is informationally complete, and this has often been taken to suggest that according to that theory the wavefunction is all there is. If we distinguish the ontological completeness of a description from its informational completeness, we can see that the best interpretations of the GRW theory must postulate more physical ontology than just the wavefunction.

Jeffrey Bub

Pavel Bóna

Hans H. Diel

The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT specifically. After such an understanding has been developed, a more precise definition of global properties, such as the completeness, computability, and extensibility of a theory, is possible and necessary. This paper addresses these subjects for theories of physics and, in particular, for QT. The basis for the definition of the completeness of a theory is the proposed definition of a "formal causal model of a physical theory". The formal model can be applied to discussions of general attributes, such as completeness, computability, and extensibility.