Related papers: $\pi$-Corrected Heisenberg Limit
The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a…
Indefinite causal orders have been shown to enable a precision of inverse square N in quantum parameter estimation, where N is the number of independent processes probed in an experiment. This surpasses the widely accepted ultimate quantum…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
Let $\phi$ be an $L^2$-normalized spherical vector in an everywhere unramified cuspidal automorphic representation of $\mathrm{PGL}_n$ over $\mathbb{Q}$ with Laplace eigenvalue $\lambda_{\phi}$. We establish explicit estimates for various…
Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is an extensive debate over the question how the sensitivity scales with the resources (such as the average photon number) and…
The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the…
Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…
Experiments near the lock-in region in maximally dissipative non-Hermitian systems, e.g., conventional laser gyroscopes near the deadband, have run up against the Petermann limit, where excess noise exactly cancels any scale-factor…
Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, this quantity acquires operational meaning only within a fully specified…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We establish a quantum Fisher information (QFI) duality for distributed quantum sensor networks with local phase encoding. For any $N$-qubit probe state, where $N$ denotes the number of sensors, $F_Q(\boldsymbol{w}^\top \boldsymbol{\theta})…
We argue that it is possible in principle to reduce the uncertainty of an atomic magnetometer by double-passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession. Numerical simulations of the quantum…
The Heisenberg uncertainty principle sets a lower bound on the sensitivity of continuous optical measurements of force. This bound, the standard quantum limit, can only be reached when a mechanical oscillator subjected to the force is…
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
We explore the performance of the metrology scheme by employing a quantum time flip during encoding, a specific case of processes with indefinite time direction, which we refer to as indefinite time directed metrology (ITDM). In the case of…
We propose a measurement setup reaching Heisenberg scaling precision for the estimation of any distributed parameter $\varphi$ (not necessarily a phase) encoded into a generic $M$-port linear network composed only of passive elements. The…