Related papers: High posterior density ellipsoids of quantum state…
In Bayesian statistics, the highest posterior density (HPD) interval is often used to describe properties of a posterior distribution. As a method for estimating confidence intervals (CIs), the HPD has two main desirable properties.…
In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. Any point estimate is necessarily "wrong" --…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Among the variety of statistical intervals, highest-density regions (HDRs) stand out for their ability to effectively summarize a distribution or sample, unveiling its distinctive and salient features. An HDR represents the minimum size set…
Quantum state tomography is the standard technique for reconstructing a quantum state from experimental data. In the regime of finite statistics, experimental data cannot give perfect information about the quantum state. A common way to…
Projected entangled pair states (PEPS) constitute a variational family of quantum states with area-law entanglement. PEPS are particularly relevant and successful for studying ground states of spatially local Hamiltonians. However,…
The outcomes of quantum mechanical experiments are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the…
For exponentially distributed lifetimes, we consider the prediction of future order statistics based on having observed the first $m$ order statistics. We focus on the previously less explored aspects of predicting: (i) an arbitrary pair of…
Quantum State Tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be…
Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set…
Despite extensive progress on image generation, common deep generative model architectures are not easily applied to lossless compression. For example, VAEs suffer from a compression cost overhead due to their latent variables. This…
Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…
Classical simulation of a programmable quantum processor is crucial in identifying the threshold of a quantum advantage. We demonstrate the simple update of projected entangled-pair states (PEPSs) in the Vidal gauge that represent random…
Estimating a joint Highest Posterior Density credible set for a multivariate posterior density is challenging as dimension gets larger. Credible intervals for univariate marginals are usually presented for ease of computation and…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions.…