Antidistinguishability of states in General Probabilistic Theories
Abstract
We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.
Related
- Multi-Time States in Quantum and Operational Probabilistic Theories: An Axiomatic Framework
- Fermionic quantum field theories as probabilistic cellular automata in three dimensions
- A New Approach to Black Hole Thermodynamics in General EMD-like Theories
- General relativity and its modifications as effective field theories of GL(4) breaking
- Simulation of quantum entangled states by classical probabilistic models
BibTeX
@misc{manna2026antidistinguishability,
title = {{Antidistinguishability of states in General Probabilistic Theories}},
author = {Satyaki Manna and Anandamay Das Bhowmik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17498},
eprint = {2609.17498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17498},
}
RIS
TY - UNPB
TI - Antidistinguishability of states in General Probabilistic Theories
AU - Satyaki Manna
AU - Anandamay Das Bhowmik
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17498
UR - https://arxiv.org/abs/2609.17498
AB - We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.
ER -