Signal detection without finite-energy limits to quantum resolution

Alfredo Luis

Quantum mechanics limit the resolution of detection schemes. Typical arrangements are based on linear processes, so that the corresponding quantum limits are usually understood as unsurpassable and ultimate. Recently it has been shown that nonlinear schemes allow signal detection and measurement with larger resolution than linear processes. In particular, this affects the quantum limits. We review the proposals introduced so far in this novel area of quantum metrology.

Juan F. Hodelin, Luca Pezzè, G. Khoury +2 more

Sara Botelho-Andrade, Peter G. Casazza, Desai Cheng +2 more

Tuvia Gefen, Maxim Khodas, Liam Paul McGuinness +2 more

Quantum spectroscopy with single two-level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by coherence of the signal and the stability of the clock used to measure time. The coherence time of the quantum probe, which can be significantly shorter, is not a major limiting factor in resolution measurements. Here, we address a similar question for spectroscopy of quantum signals, for example, a quantum sensor is used to detect a single nuclear spin. We present and analyze a novel correlation spectroscopy technique with performance that is limited by the coherence time of the target spins and the stability of the clock.

Claudio Menéndez

This work analyzes the operational status of the exact zero-temperature limit in quantum statistical mechanics under finite energy-resolution constraints. Working entirely within the standard formalism of completely positive trace-preserving (CPTP) maps, finite energy resolution is modeled through a physically motivated class of quantum channels acting as coarse-graining operations in the energy spectrum. We show that the mathematical closure defining the zero-temperature limit does not commute with operational projection. In particular, taking the limit T → 0 and applying finite-resolution coarse-graining produce inequivalent quantum states for any nonzero resolution scale. As a consequence, the exact ground state cannot be operationally represented within finite-resolution measurement regimes. The result is quantitative and operationally explicit. A trace-distance lower bound separates the ground state from the set of states obtainable through finite-resolution channels, with the bound controlled by the effective degeneracy of the low-energy subspace contained within the resolution window. This obstruction persists even as the resolution scale becomes arbitrarily small, unless infinite precision, infinite time, or unbounded physical resources are assumed. The analysis provides a precise operational formulation consistent with the third law of thermodynamics and establishes intrinsic limitations on ground-state preparation and quantum thermometry in realistic quantum platforms. The construction is minimal: it requires no modification of standard quantum mechanics and introduces no interpretational assumptions. The work is formulated within the conceptual framework of Finite-Closure Geometry (FCG), a structural program investigating the incompatibility between ideal mathematical closures and physically admissible descriptions under finite resolution. In the present case, FCG appears as an explicit non-commutativity between mathematical closure and operational projection within quantum statistical mechanics. Related work The present result is structurally complemented and generalized in Resource-Induced Non-Representability of Exact Quantum Limits (Menéndez, 2025), where the non-representability of the zero-temperature limit is derived from explicit finite physical resources (energy budget, implementation time, and control precision), independently of any specific coarse-graining model. That work shows that the obstruction identified here is not merely a consequence of finite energy resolution but a universal feature of finite-resource quantum operations. Together, these results place the phenomenon within a broader resource-theoretic and dynamical framework. Conceptual index Conceptual index of the Finite-Closure Geometry (FCG) research program: Finite Closure Geometry (FCG): A Structural Program for Global Non-Closure DOI: 10.5281/zenodo.18001440 Keywords zero-temperature limit, quantum statistical mechanics, finite energy resolution, CPTP maps, quantum coarse-graining, trace distance, ground-state preparation, third law of thermodynamics, quantum thermometry, non-commutativity, finite closure, operational limits, quantum channels, effective descriptions, finite-closure geometry

Julio I. Concha, H. Vincent Poor