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arXiv:2601.18872

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

Ladina Hausmann, Renato Renner

quant-phSubmitted Jan 26, 2026• Announced Jan 28, 2026• 0 citations
v1 · Jan 26, 2026v2 · Jun 13, 2026
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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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9 pages + 23 pages appendix

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