Related papers: Probability distributions consistent with a mixed …
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
A family of m independent identically distributed random variables indexed by a chemical potential \phi\in[0,\gamma] represents piles of particles. As \phi increases to \gamma, the mean number of particles per site converges to a maximal…
As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being…
A new class of distributions, called as normal power series (NPS), which contains the normal one as a particular case, is introduced in this paper. This new class which is obtained by compounding the normal and power series distributions,…
We construct a large class of quantum "d x d" states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic…
The convex set of quantum states of a composite $K \times K$ system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an…
The method of constructing the tomographic probability distributions describing quantum states in parallel with density operators is presented. Known examples of Husimi-Kano quasi-distribution and photon number tomography are reconsidered…
We consider a question in what condition a mixed state which can be decomposed in different ways cannot be described by a single set of hidden variables. The condition is closely related with Bell theorem.
We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability density function of bipartite entanglement and is tested on an ensemble of qubits in a variety…
Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure (mixed) one represented by a density matrix. I…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
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…
There exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
We present marginal cumulative distribution functions (CDF) for density matrices $\rho$ of fixed purity $\tfrac{1}{N}\le\mu_N(\rho)=\textrm{Tr}[\rho^2]\le 1$ for arbitrary dimension $N$. We give closed form analytic formulas for the cases…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
In the formulation of Banks, Peskin and Susskind, we show that one can construct evolution equations for the quantum mechanical density matrix $\rho$ with operators which do not commute with hamiltonian which evolve pure states into mixed…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum…