Related papers: Constructing valid density matrices on an NMR quan…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
Quantum state tomography, which aims to find the best description of a quantum state -- the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of…
New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only $O(d)$…
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…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…
Quantum state tomography (QST) aims at reconstructing the state of a quantum system. However in conventional QST the number of measurements scales exponentially with the number of qubits. Here we propose a QST protocol, in which the…
An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of…
We use a constrained convex optimization (CCO) method to experimentally characterize arbitrary quantum states and unknown quantum processes on a two-qubit NMR quantum information processor. Standard protocols for quantum state and quantum…
Maximum likelihood quantum state tomography yields estimators that are consistent, provided that the likelihood model is correct, but the maximum likelihood estimators may have bias for any finite data set. The bias of an estimator is the…
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…
Quantum state tomography, a process that reconstructs a quantum state from measurements on an ensemble of identically prepared copies, plays a crucial role in benchmarking quantum devices. However, brute-force approaches to quantum state…
The efficient quantum state reconstruction algorithm described in [P. Six et al., Phys. Rev. A 93, 012109 (2016)] is experimentally implemented on the non-local state of two microwave cavities entangled by a circular Rydberg atom. We use…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…