Decoherence in Quantum Physics

Jurjen F. Koksma, Tomislav Prokopec, Michael G. Schmidt

Fay Dowker, Steven Johnston, Sumati Surya

We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector-valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the question of the extension of the decoherence functional to the sigma algebra generated by this algebra of events. It is on the latter that the physical transition amplitudes directly give the decoherence functional. Since the full sigma algebra contains physically interesting questions, like the return question, extending the decoherence functional to these more general questions is important. We show that the decoherence functional, and hence the quantum measure, extends if and only if the associated vector measure does. We give two examples of quantum systems whose decoherence functionals do not extend: one is a unitary system with finitely many states, and the other is a quantum sequential growth model for causal sets. These examples fail to extend in the formal mathematical sense and we speculate on whether the conditions for extension are unphysically strong.

Piotr Marecki

Fay Dowker B, Steven Johnston, Sumati Surya

We point out that a quantum system with a strongly positive quantum measure or decoherence functional gives rise to a vector valued measure whose domain is the algebra of events or physical questions. This gives an immediate handle on the question of the extension of the decoherence functional to the sigma algebra generated by this algebra of events. It is on the latter that the physical transition amplitudes directly give the decoherence functional. Since the full sigma algebra contains physically interesting questions, like the return question, extending the decoherence functional to these more general questions is important. We show that the decoherence functional, and hence the quantum measure, extends if and only if the associated vector measure does. We give two examples of quantum systems whose decoherence functionals do not extend: one is a unitary system with finitely many states, and the other is a quantum sequential growth model for causal sets. These examples fail to extend in the formal mathematical sense and we speculate on whether the conditions for extension are unphysically strong.

Jincheng Zhang

This paper presents a novel theoretical model for quantum decoherence based on topological hidden-variable field theory. The core claim is to establish a model that elucidates the physical mechanism of quantum decoherence and offers a new theoretical foundation for research into quantum computation's resilience against decoherence. We posit that quantum decoherence can be viewed as an emergent phenomenon arising from interactions mediated by hidden variables within a topological hidden-variable field structure. The model utilizes mathematical tools derived from topological hidden-variable field theory to formulate and analyze the underlying physical processes. We demonstrate how the topological nature of the hidden-variable fields influences the decoherence process, providing a fresh perspective on this fundamental challenge in quantum information science. The model aims to bridge the gap between quantum mechanics and topological physics, potentially leading to innovative strategies for mitigating decoherence in quantum computing systems. Key parameters and variables are defined within the model, and the theoretical framework is presented with a focus on providing a conceptual understanding of the decoherence mechanism.

Maximilian Schlosshauer, Arthur I. Fine