The structure of states and maps in quantum theory

Gary E. Bowman

M. Asorey, Andrzej Kossakowski, Giuseppe Marmo +1 more

We analyze the structure of the subset of states generated by unital completely positive quantum maps. A witness certifying that a state does not belong to the subset generated by a given map is constructed. We analyse the representations of positive maps and their relation to quantum Perron-Frobenius theory.

Jincheng Zhang

This paper explores the intersection of quantum state geometry and information theory, proposing a novel method for encoding and transmitting quantum states through a geometric mapping framework. The core claim is that this approach simplifies the design and implementation of quantum information theory by leveraging the inherent relationships between quantum states and geometric structures. We introduce a new quantum information theory model centered around this geometric mapping, aiming to streamline the processes involved in quantum data processing and communication. The method utilizes a framework that explicitly connects the geometric properties of a quantum state with the underlying information-theoretic principles. This research investigates the potential advantages of this approach, particularly in terms of reduced computational complexity and enhanced robustness. The paper concludes with a discussion of the theoretical implications and potential applications of this geometric mapping technique.

Mirko Degli Esposti, S. Graffi

Prislac, Thomas, Echo, AI

Appendix Q – Quantum Mechanics and GUFT: A Structural Mapping of Coherence Fields Q.1. Scope and Caution Quantum mechanics (QM) is one of the most precisely tested scientific theories in history. Standard QM and quantum field theory (QFT) correctly describe an enormous range of phenomena, from atomic spectra to semiconductor devices to superconducting qubits. We are not proposing a new physics theory or “fixing” quantum mechanics. Instead, this appendix asks a narrower, safer question: How can the core structures of quantum theory—states, coherence, entanglement, measurement, decoherence—be mapped into the GUFT framework of coherence fields (Ψ = E × T, ΔS, etc.) in a way that is faithful to physics and conceptually useful? We proceed with three strict constraints: We take standard QM/QFT (as found in textbooks and reviewed sources) as non-negotiable. We treat GUFT as a descriptive overlay: a way to talk about structure and information, not an alternative dynamics. Where we draw analogies (e.g., empathy ↔ correlation), we note they are structural, not literal or magical.