On the relationship between the POVM framework and the no-signaling hypothesis
Abstract
The quantum foundations literature contains dozens of "no-signaling" arguments that rely on the Born rule or, more generally, the positive operator-valued measure (POVM) framework to show that the resources of non-relativistic quantum mechanics (NRQM) cannot be used to send superluminal signals. What these arguments typically establish, however, is not a prohibition on superluminal signaling per se, but the seemingly stronger claim that signaling at any speed between mutually isolated systems is forbidden. This paper gives a precise formulation of this claim, the no-signaling hypothesis, and investigates the following converse question: under what additional assumptions does it imply that all experimental outcome probabilities are described by POVMs? Surprisingly few are needed: given the standard NRQM representation of composite experiments and two textbook claims about marginal probabilities, the no-signaling hypothesis is equivalent to the universality of the POVM framework. More broadly, by formalizing the relevant concepts and deriving the logical relationships between them, the paper shows that the no-signaling hypothesis can be used to derive most, though not all, of the probability-generating fragment of NRQM. The resulting map of implications clarifies which common postulates of NRQM are logically interrelated and which can be modified independently.
Related
- Principal-Agent Hypothesis Testing
- An impartial Bayesian hypothesis test for audit sampling
- Currently, there are no reasons to doubt the Riemann Hypothesis: The zeta function beyond the realm of computation
- Work in progress: A Lean-verified conditional reduction of periodic Navier-Stokes regularity on T^3 to a single integrability hypothesis
- The generalized continuum hypothesis above a strongly compact cardinal
BibTeX
@misc{cavendish2026relationship,
title = {{On the relationship between the POVM framework and the no-signaling hypothesis}},
author = {Will Cavendish},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22823},
eprint = {2610.22823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22823},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the relationship between the POVM framework and the no-signaling hypothesis
AU - Will Cavendish
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.22823
UR - https://arxiv.org/abs/2610.22823
AB - The quantum foundations literature contains dozens of "no-signaling" arguments that rely on the Born rule or, more generally, the positive operator-valued measure (POVM) framework to show that the resources of non-relativistic quantum mechanics (NRQM) cannot be used to send superluminal signals. What these arguments typically establish, however, is not a prohibition on superluminal signaling per se, but the seemingly stronger claim that signaling at any speed between mutually isolated systems is forbidden. This paper gives a precise formulation of this claim, the no-signaling hypothesis, and investigates the following converse question: under what additional assumptions does it imply that all experimental outcome probabilities are described by POVMs? Surprisingly few are needed: given the standard NRQM representation of composite experiments and two textbook claims about marginal probabilities, the no-signaling hypothesis is equivalent to the universality of the POVM framework. More broadly, by formalizing the relevant concepts and deriving the logical relationships between them, the paper shows that the no-signaling hypothesis can be used to derive most, though not all, of the probability-generating fragment of NRQM. The resulting map of implications clarifies which common postulates of NRQM are logically interrelated and which can be modified independently.
ER -