What does quantum parameter estimation estimate? A no-go result for true quantity values
Abstract
We examine the conditions under which quantum parameter estimation is compatible with the concept of a ``true'' quantity value: a unique value of the estimated quantity that exists prior to and independently of measurement. While quantum parameter estimation typically assumes that the quantity to be estimated is a parameter, we argue that this assumption can be lifted, opening the way to a more general formulation of estimation that may apply even in situations where the quantity to be estimated is no longer a parameter, but instead a quantum variable susceptible to quantum fluctuations. We identify three assumptions that characterize the way estimation is often presented in the quantum metrology literature, namely, as a procedure for inferring an unknown ``true value", which is assumed to be unique and to exist prior to and independently of measurement. Using our more general framework, we prove a no-go theorem showing that the preceding assumptions are jointly incompatible with two further assumptions: the completeness of the quantum state (no `hidden variables'), and the presence of entanglement between the probe systems and the system under measurement. We note that the presence of such entanglement is a generic prediction of standard quantum theory. Consequently, if one is not willing to accept hidden variables, nor willing to modify standard quantum theory by introducing a new physical mechanism that destroys entanglement at some scale or regime, then a realist account of estimation is ultimately impossible.
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BibTeX
@misc{pienaar2026what,
title = {{What does quantum parameter estimation estimate? A no-go result for true quantity values}},
author = {Jacques L. Pienaar and Eran Tal and Asya Ciftci},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31632},
eprint = {2610.31632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31632},
}
RIS
TY - UNPB
TI - What does quantum parameter estimation estimate? A no-go result for true quantity values
AU - Jacques L. Pienaar
AU - Eran Tal
AU - Asya Ciftci
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31632
UR - https://arxiv.org/abs/2610.31632
AB - We examine the conditions under which quantum parameter estimation is compatible with the concept of a ``true'' quantity value: a unique value of the estimated quantity that exists prior to and independently of measurement. While quantum parameter estimation typically assumes that the quantity to be estimated is a parameter, we argue that this assumption can be lifted, opening the way to a more general formulation of estimation that may apply even in situations where the quantity to be estimated is no longer a parameter, but instead a quantum variable susceptible to quantum fluctuations. We identify three assumptions that characterize the way estimation is often presented in the quantum metrology literature, namely, as a procedure for inferring an unknown ``true value", which is assumed to be unique and to exist prior to and independently of measurement. Using our more general framework, we prove a no-go theorem showing that the preceding assumptions are jointly incompatible with two further assumptions: the completeness of the quantum state (no `hidden variables'), and the presence of entanglement between the probe systems and the system under measurement. We note that the presence of such entanglement is a generic prediction of standard quantum theory. Consequently, if one is not willing to accept hidden variables, nor willing to modify standard quantum theory by introducing a new physical mechanism that destroys entanglement at some scale or regime, then a realist account of estimation is ultimately impossible.
ER -