On the strangeness of quantum probabilities

Marcello Poletti

Fernando Pimentel

Once measured, a simple quantum system collapses into one state. Before that, it can be in a superposition of several states. Though these exist in a probabilistic interpretation, we often say that "the particle was in several states and collapsed to one". Although the theory and experiments agree to this, it is counter-intuitive. We give a model that delivers a possible viewpoint to overcome that strangeness. We introduce two computation ideas to interpret this apparent variation of the number of states and model its counting: computation without zero, and computing state probabilities as projections in probability dimensions of the particle positions. We bypass the physics and mathematical formalism involved, focusing not on the states and their physics, but solely on the counting of the “number of states”, given its strangeness. This model is a simplification for discussion purposes. From an arithmetical point of view, our findings suggest a conservation law for the number of states, before and after a measurement, in favor of a convergent quantum and classical physics interpretation.

Igor Evgenievich Pris

Federico Holik, Manuel Sáenz, Angel Ricardo Plastino

Osamu Hirota

In recent years, remarkable progress has been achieved in the development of quantum computers. For further development, it is important to clarify properties of errors by quantum noise and environment noise. However, when the system scale of quantum processors is expanded, it has been pointed out that a new type of quantum error, such as nonlinear error, appears. It is not clear how to handle such new effects in information theory. First of all, one should make the characteristics of the error probability of qubits clear as communication channel error models in information theory. The purpose of this paper is to survey the progress for modeling the quantum noise effects that information theorists are likely to face in the future, to cope with such nontrivial errors mentioned above. This paper explains a channel error model to represent strange properties of error probability due to new quantum noise. By this model, specific examples on the features of error probability caused by, for example, quantum recurrence effects, collective relaxation, and external force, are given. As a result, it is possible to understand the meaning of strange features of error probability that do not exist in classical information theory without going through complex physical phenomena.

David Tong

The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.