Against probability: A quantum state is more than a list of probability distributions

• URL: http://arxiv.org/abs/2601.18872v1
• Date: Mon, 26 Jan 2026 19:00:01 GMT
• Title: Against probability: A quantum state is more than a list of probability distributions
• Authors: Ladina Hausmann, Renato Renner,
• Abstract summary: The state $$ of a quantum system can be represented by a vector $mathbfP_mathM() for a set of quantum measurements.<n>Such representations appear throughout physics, for example, in correlation and in quantum foundations.
• Score: 0.5729426778193397
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The state $ρ$ of a quantum system can be represented by a vector $\mathbf{P}_{\mathcal{M}}(ρ)$ of outcome probabilities for a set of measurements $\mathcal{M}$. Such representations appear throughout physics, for example, in quantum field theory via correlation functions and in quantum foundations within generalized probabilistic frameworks. In this work, we identify an unavoidable tension: to enable operationally meaningful statements, the map ${ρ\mapsto \mathbf{P}_{\mathcal{M}}(ρ)}$ must be topologically robust $\unicode{x2013}$ preserving the notion of closeness between states. Yet, a probability representation that is topologically robust cannot simultaneously retain other essential structure, such as the subsystem structure.

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