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We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for…
The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…
We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator…
We address the problem of optimal estimation of the relative phase for two-dimensional quantum systems in mixed states. In particular, we derive the optimal measurement procedures for an arbitrary number of qubits prepared in the same mixed…
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…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
Quantum sensors are among the most promising quantum technologies, allowing to attain the ultimate precision limit for parameter estimation. In order to achieve this, it is required to fully control and optimize what constitutes the…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
Quantum phase estimation is fundamental to advancing quantum science and technology. While much of the research has concentrated on estimating a single phase, the simultaneous estimation of multiple phases can yield significantly enhanced…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
We consider the problem of estimating multiple phases using a multi-mode interferometer. In this setting we show that while global strategies with multi-mode entanglement can lead to high precision gains, the same precision enhancements can…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…
We consider a scheme of quantum teleportation where a receiver has multiple (N) output ports and obtains the teleported state by merely selecting one of the N ports according to the outcome of the sender's measurement. We demonstrate that…
We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple-phase interferometry and stress insufficiency of the analysis based solely on the concept of quantum Fisher information. We show that the…