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Recently, the Hilbert-Schmidt speed, as a special class of quantum statistical speed, has been reported to improve the interferometric phase in single-parameter quantum estimation. Here, we test this concept in the multiparameter scenario…

We investigate how the Hilbert-Schmidt speed (HSS), a special type of quantum statistical speed, can be exploited as a powerful and easily computable tool for quantum phase estimation in a $n$-qubit system. We find that, when both the HSS…

We present a method to estimate the probabilities of outcomes of a quantum observable, its mean value, and higher moments by measuring any other observable. This method is general and can be applied to any quantum system. In the case of…

We address parameter estimation in two-level systems exhibiting level anti-crossing and prove that universally optimal strategies for parameter estimation may be designed, that is, we may find a parameter independent measurement scheme…

We show that the time dependence of mean value of a physical quantity is related with the transition energies of a quantum system. In the case when the operator of a physical quantity anticommutes with the Hamiltonian of a system, studies…

We propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system's dynamics, but not all of it, one can use the measured energy to determine many other quantities, such…

Effective nonlinear optical interactions are essential for many applications in modern photonics. In this paper, we investigate the role of the nonlinear response of a material to improve quantum metrology. In particular, the collective…

We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…

We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric…

The traditional framework of quantum metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein can be infeasible in practice. Here, we…

In many-body quantum systems, the quantum Fisher information an observer can obtain is susceptible to decoherence. Consequently, quantum enhanced metrology, such as Heisenberg scaling, cannot usually be achieved. We show, via two distinct…

Relevant metrological scenarios involve the simultaneous estimation of multiple parameters. The fundamental ingredient to achieve quantum-enhanced performances is based on the use of appropriately tailored quantum probes. However, reaching…

We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…

We report a simple and pure data-driven method to find new energy levels of quantum many-body systems only from observed line wavelengths. In our method, all the possible combinations are computed from known energy levels and wavelengths of…

Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum…

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. A recently developed quantum statistical (QS) approach that takes the formation of…

The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…

Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various…

We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…

In this paper we introduce the energy efficiency as a new metric for evaluating both hardware platforms based on Graphic Processor Units (GPU), and algorithm optimisations at High Energy Physics (HEP) experiments. We develop a method to…