Related papers: Explicit form of the Bayesian posterior estimate o…
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…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
In the paper the Bayesian and the least squares methods of quantum state tomography are compared for a single qubit. The quality of the estimates are compared by computer simulation when the true state is either mixed or pure. The fidelity…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed…
The informational approach to continuous quantum measurement is derived from POVM formalism for a mesoscopic scattering detector measuring a charge qubit. Quantum Bayesian equations for the qubit density matrix are derived, and cast into…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…
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 quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Bayesian inverse problem on an infinite dimensional separable Hilbert space with the whole state observed is well posed when the prior state distribution is a Gaussian probability measure and the data error covariance is a cylindric…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…
Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
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…