Related papers: Constructing valid density matrices on an NMR quan…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit…
We show that the method of maximum likelihood (MML) provides us with an efficient scheme for reconstruction of quantum channels from incomplete measurement data. By construction this scheme always results in estimations of channels that are…
The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that…
Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization for state reconstruction, we…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
To improve the efficiency of the state tomography strategy via weak value, we have searched the optimal coupling strength between the system and measuring device. For an arbitrary d-dimensional quantum system, the optimal strengths being…
We show that the method of maximum-likelihood estimation, recently introduced in the context of quantum process tomography, can be applied to the determination of Mueller matrices characterizing the polarization properties of classical…
We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and maximum-likelihood principle. In the…
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…
Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often…
Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting…
Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic…
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…
Quantum state estimation (or state tomography) is an indispensable task in quantum information processing. Because full state tomography that determines all elements of the density matrix is computationally demanding, one usually takes the…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…