Related papers: Numerical Bayesian quantum-state assignment for a …
This paper offers examples of concrete numerical applications of Bayesian quantum-state-assignment methods to a three-level quantum system. The statistical operator assigned on the evidence of various measurement data and kinds of prior…
Recently quantum prediction problem was proposed in the Bayesian framework. It is shown that Bayesian predictive density operators are the best predictive density operators when we evaluate them by using the average relative entropy based…
In this paper we are interested to model quantum signal by statistical signal processing methods. The Gaussian distribution has been considered for the input quantum signal as Gaussian state have been proven to a type of important robust…
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…
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…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
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…
In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a…
Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
We derive an expression for a density operator estimated via Bayesian quantum inference in the limit of an infinite number of measurements. This expression is derived under the assumption that the reconstructed system is in a pure state. In…
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…
We present an approach to Bayesian mean estimation of quantum states using hyperspherical parametrization and an experiment-specific likelihood which allows utilization of all available data, even when qubits are lost. With this method, we…
The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
In this work we introduce a general scheme for measurement based quantum computation in continuous variables. Our approach does not necessarily rely on the use of ancillary cluster states to achieve its aim, but rather on the detection of a…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…
An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure…
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically,…