Related papers: Estimation of Gaussian quantum states
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
Estimation of parameters is a pivotal task throughout science and technology. Quantum Cram\'{e}r-Rao bound provides a fundamental limit of precision allowed to achieve under quantum theory. For closed quantum systems, it has been shown how…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
We investigate whether collider experiments can reach the quantum limit of precision, defined by the quantum Fisher information (QFI), using only classical observables such as particle momenta. As a case study, we focus on the…
To any parametric family of states of a finite level quantum system we associate a space of Fisher maps and introduce the natural notions of Cram\'er-Rao-Bhattacharya tensor and Fisher information form. This leads us to an abstract…
Quantum Fisher information (QFI) of the reduced two-atom state is employed to capture the quantum criticality of the superradiant phase transition in the Dicke model in the infinite size and finite-$N$ systems respectively. The analytical…
Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…
The power of quantum sensing rests on its ultimate precision limit, quantified by the quantum Cramer-Rao bound (QCRB), which can surpass classical bounds. In multi-parameter estimation, the QCRB is not always saturated as the quantum nature…
We formulate the problem of determining the volume of the set of Gaussian physical states in the framework of information geometry. That is, by considering phase space probability distributions parametrized by the covariances and supplying…
Quantifying measurement precision in quantum systems is vital for advancing quantum technologies such as sensing, communication, and computation. The quantum Fisher information (QFI) sets the ultimate precision bound in Hermitian systems;…
We introduce a canonical decomposition of the quantum Fisher information (QFI) for centered multimode Gaussian states into two additive pieces: an even part that captures changes in the symplectic spectrum and an odd part associated with…
Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian…
Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
Photon-subtracted and photon-added Gaussian states are amongst the simplest non-Gaussian states that are experimentally available. It is generally believed that they are some of the best candidates to enhance sensitivity in parameter…
Understanding how well future cosmological experiments can reconstruct the mechanism that generated primordial inhomogeneities is key to assessing the extent to which cosmology can inform fundamental physics. In this work, we apply a…
The single-mode Dicke model is well-known to undergo a quantum phase transition from the so-called normal phase to the supperradiant phase (hereinafter called the "superradiant quantum phase transition"). Normally, quantum phase transitions…
In quantum parameter estimation, the quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit on the precision achievable with unbiased estimators. It relates the uncertainty in estimating a parameter to the inverse of the quantum Fisher…
The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem…
Precision measurements with quantum systems rely on our ability to trace the differences between experimental signals to variations in unknown physical parameters. In this Letter we derive the Fisher information and the ensuing Cramer-Rao…