Quantum information processing: a new light on the Q-formalism and Q-foundations

Matty J. Hoban

Abstract Understanding the role of causality in quantum theory is a growing research direction in quantum information and the foundations of quantum theory. One particular area is to understand generalizations of quantum theory where there is an indefinite causal order between various operations. Building on recent work developing the process matrix formalism, Araújo et al (2015 New J. Phys. 17 102001 ) give formal tools to analyse how causally indefinite processes can be by drawing inspiration from entanglement theory. This approach draws together concepts in quantum information with more speculative ideas in the foundations of quantum theory.

Dimitris G. Angelakis, Matthias Christandl, ARTUR K. EKERT +2 more

Jincheng Zhang

Quantum information theory, a foundational field within quantum computing and cryptography, relies heavily on the precise manipulation and analysis of quantum states. Traditional approaches often struggle to adequately represent and quantify the complexities inherent in these states. This paper proposes a novel framework based on hypergeometric distributions to formalize the mathematical foundations of quantum information theory, offering a rigorous and powerful tool for predicting and analyzing quantum phenomena. Hypergeometric distributions, a specialized distribution in probability theory, provide a natural and efficient way to model the correlated nature of quantum states, leading to a more robust and adaptable mathematical foundation. The core mechanism involves developing new mathematical tools to quantify fidelity and entanglement, thereby facilitating the design of quantum algorithms. This work aims to bridge the gap between theoretical concepts and practical applications, potentially unlocking new algorithmic possibilities and pushing the boundaries of quantum information processing.

Giulio Chiribella

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

Ian A. Walmsley

There are many kinds of quantum light source, each producing a distinct kind of quantum light. ‘Quantum light’ first considers sources that generate the primitive quantum state of light—a single photon. Such light sources are the workhorses of the field of quantum optics, which uses the quantum mechanical features of light to explore the foundations of quantum physics, as well as to enable new kinds of information processing technologies. Squeezed light and quantum entanglement are also discussed. Entanglement is a very weird concept, but it enables a raft of information processing approaches that cannot be replicated by sending classical waves back and forth, and promises a future quantum Internet.