Related papers: Haar-random and pretty good measurements for Bayes…
The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context of compact quantum groups. We provide a…
Ultrafast dynamical processes in photoexcited molecules can be observed with pump-probe measurements, in which information about the dynamics is obtained from the transient signal associated with the excited state. Background signals…
In this paper we extend the construction of random walks with a prescribed Poisson boundary to the case of measures in the class of a generalized Gibbs state. The price for dropping the $\alpha$-quasiconformal assumptions is that we must…
Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
In a recently demonstrated quantum-state tomography scheme [Phys. Rev. Lett. 124, 010405 (2020)], a random control field is locally applied to a multipartite system to reconstruct the full quantum state of the system through…
We report an experimental realization of an adaptive quantum state tomography protocol. Our method takes advantage of a Bayesian approach to statistical inference and is naturally tailored for adaptive strategies. For pure states we observe…
In this paper we study the Minimum Error Discrimination problem (MED) for ensembles of linearly independent (LI) states. We define a bijective map from the set of those ensembles to itself and we show that the Pretty Good Measurement (PGM)…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
The properties of the generalized Waring distribution defined on the non negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then…
We describe a simple method for certifying that an experimental device prepares a desired quantum state rho. Our method is applicable to any pure state rho, and it provides an estimate of the fidelity between rho and the actual (arbitrary)…
It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered…
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary…
When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
Statistical estimates from survey samples have traditionally been obtained via design-based estimators. In many cases, these estimators tend to work well for quantities such as population totals or means, but can fall short as sample sizes…
In this paper we investigate repeated weak measurements,without post-selection, on a \emph{single copy} of an \emph{unknown} quantum state. The resulting random walk in state space is precisely characterised in terms of joint probabilities…
Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…