Recently, we find a physical limit on energy consumption of quantum metrology, and demonstrate that it essentially arises from the erasure of quantum Fisher information (QFI) which determines the best achievable measurement precision. Here, we provide more details in order to further elaborate the essence of this principle.
The heat dissipation in quantum metrology represents not only an unavoidable problem towards practical applications of quantum sensing devices but also a fundamental relationship between thermodynamics and quantum metrology. However, a general thermodynamic principle which governs the rule of energy consumption in quantum metrology, similar to Landauer's principle for heat dissipation in computations, has remained elusive. Here, we establish such a physical principle for energy consumption in order to achieve a certain level of measurement precision in quantum metrology, and show that it is intrinsically determined by the erasure of quantum Fisher information. The principle provides a powerful tool to investigate the advantage of quantum resources, not only in measurement precision but also in energy efficiency. It also serves as a bridge between thermodynamics and various fundamental physical concepts related in quantum physics and quantum information theory.
Abstract Establishing a concrete link between quantum information measures and thermodynamic quantities remains a significant challenge in contemporary research. This paper presents novel contributions exploring three key aspects. First, we investigate the relationship between quantum Fisher information (QFI) and work and heat exchange during a feedback control measurement cycle, unveiling a quantitative interplay between energy and information. Second, we demonstrate the behavior of heat exchange with the environment at the point of maximum estimation precision, and a direct relation that links the von Neumann entropy in systems with a large number of microstates with the precision of the estimation through QFI, shedding light on the thermodynamic signature of optimal quantum parameter estimation, bridging quantum metrology, and statistical thermodynamics in the context of high-dimensional stochastic systems. Finally, we propose a method for detecting entanglement based on thermodynamic work, introducing a framework to identify entanglement through energy considerations in a quantum system. Together, these findings advance our understanding of the intersection between quantum information theory and quantum thermodynamics, providing an additional foundation for future research.
Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.
In Phys. Rev. Lett. 128, 200501 (2022) the authors consider the thermodynamic cost of quantum metrology. One of the main results is S≥log(2)∥hλ∥−2FQ[ψλ], which purports to relate the Shannon entropy S of an optimal measurement (i.e., in the basis of the symmetric logarithmic derivative) to the quantum Fisher information FQ of the pure state ∣ψλ⟩. However, we show that in the setting considered by the authors we have S=log(2) and ∥hλ∥2=maxψλFQ[ψλ], so that their inequality reduces to the trivial inequality maxψλFQ[ψλ]≥FQ[ψλ], and does not in fact relate the entropy S to the quantum Fisher information. Moreover, for pure state quantum metrology, there exist optimal measurements (though not in the basis of the symmetric logarithmic derivative) for which 0≤S≤log(2), leading to violations of the inequality for some states ∣ψλ⟩.
Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, such an interpreta- tion is only justified within a fully specified inference framework that consistently incorporates state preparation, measurement design, resource accounting, estimator construction, prior information, and finite data effects. Here we develop an operational, end-to-end framework for quantum sensing under finite resources and identify general principles required for meaningful performance assess- ment. A central conceptual point is that the relevant unit of estimation is not a single detection event, but the complete data set required to construct a consistent estimator. Rather than relying on abstract statistical formalism, we analyze a set of paradigmatic and experimentally relevant ex- amples that expose common pitfalls in widely discussed quantum sensing strategies. These include quantum interferometry, sensing with squeezed states, and criticality-inspired protocols. Our results clarify when large Fisher information or nonclassical resources translate into genuine metrological advantage, and when they do not. They further provide a practical methodology for designing and evaluating quantum sensing protocols under realistic experimental constraints.
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information (QFI) yields results that are asymptotically equivalent to those from the rigorous Bayesian approach, provided generic uncorrelated noise is present in the setup. At the same time, we show that for the problem of decoherence-free phase estimation this equivalence breaks down, and the achievable estimation uncertainty calculated within the Bayesian approach is larger by a factor of π than that predicted from the QFI even in the large prior knowledge (small parameter fluctuation) regime, where the QFI is conventionally regarded as a reliable figure of merit. We conjecture that an analogous discrepancy is present in the arbitrary decoherence-free unitary parameter estimation scheme, and propose a general formula for the asymptotically achievable precision limit. We also discuss protocols utilizing states with an indefinite number of particles, and show that within the Bayesian approach it is legitimate to replace the number of particles with the mean number of particles in the formulas for the asymptotic precision, which as a consequence provides another argument for proposals based on the properties of the QFI of indefinite particle number states leading to sub-Heisenberg precisions not being practically feasible.