Related papers: Parameterizing density matrices for composite quan…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
In this thesis we study the behavior of bipartite entanglement of a large quantum system, by analyzing the distribution of the Schmidt coefficients of the reduced density matrix. Applying the general methods of classical statistical…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
We introduce a class of inequalities based on low order correlations of operators to detect entanglement in bipartite systems. The operators may either be Hermitian or non-Hermitian and are applicable to any physical system or class of…
We show that all density operators of 2$\times N$--dimensional quantum systems that remain invariant after partial transposition with respect to the first system are separable. Based on this criterion, we derive a sufficient separability…
We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…
We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…
We extend an operational characterization of entanglement in terms of stabilizer groups from pure states to mixed states. For a density matrix $\rho_{AB}$, a stabilizer is a factorized unitary matrix $u_A \otimes u_B$ that, under…
We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed…
We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing…
We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations we define a straightforward procedure for…
We discuss a scheme for reconstructing experimentally the diagonal elements of the density matrix of quantum optical states. Applications to PDC heralded photons, multi-thermal and attenuated coherent states are illustrated and discussed in…