Against probability: A quantum state is more than a list of probability distributions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917224706473984 |
|---|---|
| author | Hausmann, Ladina Renner, Renato |
| author_facet | Hausmann, Ladina Renner, Renato |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18872 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Against probability: A quantum state is more than a list of probability distributions Hausmann, Ladina Renner, Renato Quantum Physics 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. |
| title | Against probability: A quantum state is more than a list of probability distributions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.18872 |