Related papers: Dichotomic probability representation of quantum s…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…
The quantum state of a $d$-dimensional system can be represented by the $d^2$ probabilities corresponding to a SIC-POVM, and then this distribution of probability can be represented by a vector of $\R^{d^2-1}$ in a simplex, we will call…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
Analytic expressions for the probability density distribution of the linear entropy and the purity are derived for bipartite pure random quantum states. The explicit distributions for a state belonging to a product of Hilbert spaces of…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
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…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
The notion of weighted quantum entropy is reviewed and considered for bipartite and noncomposite quantum systems. The known for the weighted entropy information inequality (subadditivity condition) is extended to the case of indivisible…
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.…
We discuss the possibility to formulate the dynamics of spin states described by the Schrodinger equation for pure states and the von Neumann equation (as well as the GKSL equation) for mixed states in the form of quantum kinetic equations…
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
The q-deformed entropies of quantum and classical systems are discussed. Standard and q-deformed entropic inequalities for X - states of the two-qubit and a state of single qudit with $j=3/2$ are presented.
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
The states of the qubit, the basic unit of quantum information, are $2 \times 2$ positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the…