An operational characterization of finite-dimensional quantum theory
Abstract
A key goal in the foundations of quantum mechanics is to identify operational constraints characterizing physical theories. Bell inequalities do so for classical probability theory, while Tsirelson's bound provides a first step for quantum mechanics. Here, we address the dual question: Can one certify that all correlations predicted by quantum theory are actually realizable? In this work, we construct a finite number of two-body correlations such that the only probabilistic theory that (1) realizes them, and (2) does so in a way that is stable under iterated teleportation, is quantum theory. For n quantum systems of dimension d each, Condition (1) can be verified using poly(d,n) measurement settings. Condition (2) may be understood as a hierarchy of tests, one for each number N of teleportation steps. There is thus a sense in which finite-dimensional quantum theory can be self-tested. In particular, one can certify the existence of Bell inequality violations larger than any that have been directly observed.
Related
- Operational theory for photonic circuits: generalizing linear optics beyond quantum theory
- Finite-size scaling theory of Rényi thermal entropy for second-order, first-order, and weakly first-order quantum phase transitions
- Quantum 6j-symbols arising from a subfactor of finite index and finite depth and the zipper condition for 4-tensors in two-dimensional topological order
- Quantum geometric bounds at finite temperature for one-dimensional chiral systems
- Finite-temperature Quantum Quasinormal Mode Theory for Spatiotemporally-resolved Dissipative Cavity Quantum Magnonics
BibTeX
@misc{dmello2026operational,
title = {{An operational characterization of finite-dimensional quantum theory}},
author = {Lionel J. Dmello and Xiangling Xu and Marc-Olivier Renou and David Gross},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03694},
eprint = {2610.03694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03694},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An operational characterization of finite-dimensional quantum theory
AU - Lionel J. Dmello
AU - Xiangling Xu
AU - Marc-Olivier Renou
AU - David Gross
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.03694
UR - https://arxiv.org/abs/2610.03694
AB - A key goal in the foundations of quantum mechanics is to identify operational constraints characterizing physical theories. Bell inequalities do so for classical probability theory, while Tsirelson's bound provides a first step for quantum mechanics. Here, we address the dual question: Can one certify that all correlations predicted by quantum theory are actually realizable? In this work, we construct a finite number of two-body correlations such that the only probabilistic theory that (1) realizes them, and (2) does so in a way that is stable under iterated teleportation, is quantum theory. For n quantum systems of dimension d each, Condition (1) can be verified using poly(d,n) measurement settings. Condition (2) may be understood as a hierarchy of tests, one for each number N of teleportation steps. There is thus a sense in which finite-dimensional quantum theory can be self-tested. In particular, one can certify the existence of Bell inequality violations larger than any that have been directly observed.
ER -