Quantum Dynamics Happens Only on Paper: QBism's Account of Decoherence

• URL: http://arxiv.org/abs/2312.14112v2
• Date: Fri, 17 May 2024 20:53:16 GMT
• Title: Quantum Dynamics Happens Only on Paper: QBism's Account of Decoherence
• Authors: John B. DeBrota, Christopher A. Fuchs, Ruediger Schack,
• Abstract summary: QBism has long recognized quantum states, POVM elements, Kraus operators, and even unitary operations to be cut from the same cloth. We present a representation theorem based on van Fraassen's reflection principle.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: QBism has long recognized quantum states, POVM elements, Kraus operators, and even unitary operations to be cut from the same cloth: They express aspects of an agent's personal belief system concerning the consequences (for her) of actions she might take on her external world. Such action-consequence pairs have conventionally been called "quantum measurements." The calculus of quantum theory is then viewed as an empirically motivated addition to Bayesian decision theory when brought to this notion of measurement. This radical approach has allowed QBism to eliminate conceptual problems that plague other interpretations of quantum mechanics. However, one issue has remained elusive: If a QBist does not believe in the existence of an ontic (agent-independent) dynamical variable evolving over time, why would there be any constraints on her quantum-state assignment in the absence of performing a measurement? Why would she introduce unitary or open-system quantum dynamics at all? Here, we present a representation theorem based on van Fraassen's reflection principle to answer these questions. Simply put, an agent's assignment of quantum dynamics represents her belief that a measurement action she is contemplating would not change her current odds for future gambles. A corollary to this approach is that one can make sense of "open-system dynamics" without introducing an "environment with a measurement record" as is common in decoherence accounts of quantum measurement. Instead, the QBist understanding of decoherence rests entirely on an agent's beliefs about the system of interest (not system plus environment) and her judgments about measurements she might perform on that system. More broadly, this result establishes QBism's contention that measurement itself is the central concept of quantum theory and thus the framework upon which any future QBist ontology must hang.

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