Related papers: Triangle geometry for qutrit states in the probabi…

We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…

Any set of pure states living in an given Hilbert space possesses a natural and unique metric --the Haar measure-- on the group $U(N)$ of unitary matrices. However, there is no specific measure induced on the set of eigenvalues $\Delta$ of…

Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the…

We present a generalization to 3-qubits of the standard Bloch sphere representation for a single qubit and of the 7-dimensional sphere representation for 2 qubits presented in Mosseri {\it et al.}\cite{Mosseri2001}. The Hilbert space of the…

Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…

A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states…

A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…

The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and consequently house a fractional number of electrons (net charge). The natural framework describing the quantum…

A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…

Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…

We propose a method for constructing multi-qubit entangled quantum states representing weighted tripartite graphs. An expression for the entanglement distance for multi-qubit states corresponding to arbitrary tripartite graph structures is…

We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation…

We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt distance to the convex hull of spin coherent states. We derive its analytic expression in the case of pure states as a function of the smallest eigenvalue of the…

Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept,…

We show how the Majorana representation can be used to express the pure states of an N-qubit system as points on the Bloch sphere. We compare this geometrical representation of N-qubit states with an alternative one, proposed recently by…

Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…

Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…

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…

Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…

We study the invariant theory of trilinear forms over a three-dimensional complex vector space, and apply it to investigate the behaviour of pure entangled three-partite qutrit states and their normal forms under local filtering operations…