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.

20 pages, 2 figures. To appear in Coherentist Approaches to Quantum Metrology, Routledge Studies in the Philosophy of Mathematics and Physics (forthcoming)

arXiv:2610.31632 [quant-ph]

(or arXiv:2610.31632v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.31632 arXiv-issued DOI via DataCite (pending registration)