Related papers: Schmidt decomposition and multivariate statistical…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…
A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
We study the mathematical structures and relations among some quantities in the theory of quantum entanglement, such as separability, weak Schmidt decompositions, Hadamard matrices etc.. We provide an operational method to identify the…
We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The…
We investigate the procedure of Schmidt modes extraction in systems with continuous variables. An algorithm based on singular value matrix decomposition is applied to the study of entanglement in an "atom-photon" system with spontaneous…
We theoretically investigate the spectral entanglement of a multiphoton source generated from the cascade emissions in the cascaded cold atomic ensembles.\ This photon source is highly directional, guaranteed under the four-wave mixing…
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 introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
The Schmidt number is an important kind of characterization of quantum entanglement. Quantum states with higher Schmidt numbers demonstrate significant advantages in various quantum information processing tasks. By deriving a class of…