Related papers: Conservative classical and quantum resolution limi…
We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cram\'er--Rao-type…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
A recently identified class of receivers which demultiplex an optical field into a set of orthogonal spatial modes prior to detection can surpass canonical diffraction limits on spatial resolution for simple incoherent imaging tasks.…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
Informationally overcomplete POVMs are known to outperform minimally complete measurements in many tomography and estimation tasks, and they also leave a purely classical freedom in shadow tomography: the same observable admits infinitely…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
Nonlinear quantum metrology schemes can lead to faster than Heisenberg limited scalings for the measurement uncertainty. We study a Michelson interferometer embedded in a Kerr medium [Luis and Rivas, Phys. Rev. A 92, 022104 (2015)] that…
The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the…
This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection…
Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is…
How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory the variance of an unbiased parameter estimator is bounded from below by the inverse of…
Image based diagnostics are interpreted in the context of spatial resolution. The same is true for tomographic image reconstruction. Current empirically driven approaches to quantify spatial resolution rely on a deterministic formulation…
We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be…
We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of…
The development of high-resolution, large-baseline optical interferometers would revolutionize astronomical imaging. However, classical techniques are hindered by physical limitations including loss, noise, and the fact that the received…
Decoherence often happens in the quantum world. We try to utilize quantum dephasing to build an optimal thermometry. By calculating the Cram$\acute{e}$r-Rao bound, we prove that the Ramsey measurement is the optimal way to measure the…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
Measurements of quantum states form a key component in quantum-information processing. It is therefore an important task to compare measurements and furthermore decide if a measurement strategy is optimal. Entropic quantities, such as the…
We implement a general imaging method by measuring the complex degree of coherence using linear optics and photon number resolving detectors. In the absence of collective or entanglement assisted measurements, our method is optimal over a…
We develop a classical shadow tomography protocol utilizing the randomized measurement scheme based on hybrid quantum circuits, which consist of layers of two-qubit random unitary gates mixed with single-qubit random projective…