Related papers: From quantum Bayesian inference to quantum tomogra…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
The expression for the density operator of the damped harmonic oscillator is derived from the master equation in the framework of the Lindblad theory for open quantum systems. Then the von Neumann entropy and effective temperature of the…
We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves performing randomized measurements on a quantum processor…
The paper discusses the reconstruction of potentials for quantum systems at finite temperatures from observational data. A nonparametric approach is developed, based on the framework of Bayesian statistics, to solve such inverse problems.…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
We describe regularized methods for image reconstruction and focus on the question of hyperparameter and instrument parameter estimation, i.e. unsupervised and myopic problems. We developed a Bayesian framework that is based on the \post…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not…
We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a non-abelian operator algebra, which provides a representation of…
For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…
The knowledge of the density matrix of a quantum state plays a fundamental role in several fields ranging from quantum information processing to experiments on foundations of quantum mechanics and quantum optics. Recently, a method has been…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
We reconstruct quantum mechanics by introducing "information operators" and excluding the concept of wave functions. Multiple information operators simultaneously describe a single system and continuously develop in time even in the process…
We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators…
We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the…