Related papers: Quantum state estimation when qubits are lost: A n…
This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation…
We present a joint-measurement uncertainty relation for a pair of mean square deviations of canonical variables averaged over Gaussian distributed quantum optical states. Our Bayesian formulation is free from the unbiasedness assumption,…
We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state new information is continually mapped onto the measured…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows…
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…
It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal…
We introduce a genetic algorithm that designs quantum optics experiments for engineering quantum states with specific properties. Our algorithm is powerful and flexible, and can easily be modified to find methods of engineering states for a…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
Current quantum computers have the potential to overcome classical computational methods, however, the capability of the algorithms that can be executed on noisy intermediate-scale quantum devices is limited due to hardware imperfections.…
We introduce an efficient and accurate readout measurement scheme for single and multi-qubit states. Our method uses Bayesian inference to build an assignment probability distribution for each qubit state based on a reference…
A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…
The optimal estimation of a quantum mechanical 2-state system (qubit) - with N identically prepared qubits available - is obtained by measuring all qubits simultaneously in an entangled basis. We report the experimental estimation of qubits…
Gaussian states are of increasing interest in the estimation of physical parameters because they are easy to prepare and manipulate in experiments. In this article, we derive formulae for the optimal estimation of parameters using two- and…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure.…
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 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…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…