Related papers: One-qubit reduced states of a pure many-qubit stat…

We present a necessary and sufficient condition for three qutrit density matrices to be the one-particle reduced density matrices of a pure three-qutrit quantum state. The condition consists of seven classes of inequalities satisfied by the…

If a pure state of a qubit pair is developed over the four basis states, it is known that an equality between the four coefficients of that development exists if and only if that state is unentangled. This paper considers an arbitrary pure…

We derive necessary and sufficient conditions for the LU-equivalence of two general (pure or mixed) $n$-qubit states as well as we determine the local unitary operators connecting them. Almost all relevant information is contained in the…

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is…

We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…

In a system of n quantum particles, we define a measure of the degree of irreducible n-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of (n-1) particles. In the case of almost all…

In this paper, we discuss the partial separability and its criteria problems of multipartite qubit mixed-states. First we strictly define what is the partial separability of a multipartite qubit system. Next we give a reduction way from…

We prove a set of tight entanglement inequalities for arbitrary $N$-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper…

We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if these states are orthogonal. The sufficient and necessary condition when nonorthogonal quantum mixed states can be unambiguously…

This paper characterizes two forms of separability of pure states of systems of n qubits: (i) into a tensor product of n qubit states, and (ii), into a tensor product of 2 subsystems states of p and q qubits respectively with p+q=n. For…

We propose novel mixed states in two qubits, ``maximally entangled mixed states'', which have a property that the amount of entanglement of these states cannot be increased further by applying any unitary operations. The property is proven…

We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of $n-1$ particles. The method of providing of the…

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…

We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is…

We study the conditions when mixtures of entangled pure states with maximally mixed one-qudit reduced density matrices remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to…

A simplified expression of concurrence for two-qubit mixed state having no more than three non-vanishing eigenvalues is obtained. Basing on SU(2) coherent states, the amount of entanglement of two-qubit pure states is studied and conditions…

The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability…

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd…

We give necessary conditions for the mixing problem in bipartite case, which are independent of eigenvalues and based on algebraic-geometric invariants of the bipartite states. One implication of our results is that for some special…