Related papers: Haar-random and pretty good measurements for Bayes…
Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact…
In this note, we extend the characterization of dyadic Lipschitz regularity of functions to non-atomic probability spaces, using generalized Haar systems.
We investigate schemes for Hamiltonian parameter estimation of a two-level system using repeated measurements in a fixed basis. The simplest (Fourier based) schemes yield an estimate with a mean square error (MSE) that decreases at best as…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
Given a single copy of a mixed state of the form \rho=\lambda\rho_1+(1-\lambda)\rho_2, what is the optimal measurement to estimate the parameter \lambda, if \rho_1 and \rho_2 are known? We present a general strategy to obtain the optimal…
We adopt the concept of the composite parameterization of the unitary group U(d) to the special unitary group SU(d). Furthermore, we also consider the Haar measure in terms of the introduced parameters. We show that the well-defined…
The construction of physically relevant low dimensional state models, and the design of appropriate measurements are key issues in tackling quantum state tomography for large dimensional systems. We consider the statistical problem of…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…
We investigate randomized benchmarking in a general setting with quantum gates that form a representation, not necessarily an irreducible one, of a finite group. We derive an estimate for the average fidelity, to which experimental data may…
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show…
We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…
A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost-effective method, ranked set sampling enables us to incorporate…
The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates…
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$.…
Integrated quantum photonic circuits are becoming increasingly complex. Accurate calibration of device parameters and detailed characterization of the prepared quantum states are critically important for future progress. Here we report on…