Related papers: Freudenthal ranks: GHZ vs. W
We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end we derive a new decomposition for arbitrary 3-qubit states which is characterized by five parameters (up to local…
The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single mode approximation. Due to acceleration the quantum coherence is…
Quatum nonlocality as a valuable resource is of vital importance in quantum information processing. The characterization of the resource has been extensively investigated mainly for pure states, while relatively less is know for mixed…
We find that multidimensional determinants "hyperdeterminants", related to entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3 qubits, respectively), are derived from a duality between entangled states and separable…
In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite…
Mermin inequalities are derived for systems of three-state particles (qutrits) employing three local measurement settings. These establish perfect correlations which violate local realistic bounds more strongly than those previously…
We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball…
We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space…
Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the…
In this paper, we study the ordering states with Tsallis relative $\alpha$-entropies of coherence and $l_{1}$ norm of coherence for single-qubit states. We show that any Tsallis relative $\alpha$-entropies of coherence and $l_{1}$ norm of…
We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the $W$-class, which only possess globally distributed pairwise entanglement as measured by the…
Any pure three-qubit state is uniquely characterized by one phase and four positive parameters. The geometric measure of entanglement as a function of state parameters can have different expressions. Each of expressions has its own…
We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three…
Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state space of the system; the quantum state…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
We investigate leader election problem via ranking within self-stabilising population protocols. In this scenario, the agent's state space comprises $n$ rank states and $x$ extra states. The initial configuration of $n$ agents consists of…
The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for n players demonstrating this non-local property of…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object…
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over…
In this paper we analyze the canonical forms into which any pure three-qubit state can be cast. The minimal forms, i.e. the ones with the minimal number of product states built from local bases, are also presented and lead to a complete…