Related papers: Adaptive Bayesian Quantum Tomography
We introduce a simple protocol for adaptive quantum state tomography, which reduces the worst-case infidelity between the estimate and the true state from $O(N^{-1/2})$ to $O(N^{-1})$. It uses a single adaptation step and just one extra…
Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…
Quantum scale estimation, as introduced and explored here, establishes the most precise framework for the estimation of scale parameters that is allowed by the laws of quantum mechanics. This addresses an important gap in quantum metrology,…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…
Tomographic reconstruction of the many-body quantum state of a scalable qubit system is of paramount importance in quantum computing technologies. However, conventional approaches which use tomographically orthogonal base measurements…
Quantum metrology seeks to leverage the richness of quantum systems for making better measurements than are possible using only classical resources in order to gain a ``quantum advantage''. Quantum metrology schemes must also be resilient…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…
Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal…
We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…
The precision limit in quantum state tomography is of great interest not only to practical applications but also to foundational studies. However, little is known about this subject in the multiparameter setting even theoretically due to…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
The optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the…
Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori knowledge of the experimentalists makes this…
We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this…
Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many…