Establishing long-distance quantum entanglement, i.e., entanglement transmission, in networks (QN) is a key and timely challenge for developing efficient communication. Traditional comprehension based on classical percolation assumes necessary condition successful transmission between any two infinitely distant nodes: they must be connected by at least path of perfectly entangled states (single...

We propose concurrence classes for general pure multipartite states based on an orthogonal complement of a positive operator valued measure on quantum phase. In particular, we construct W m class, GHZ, and GHZ class concurrences for general pure m-partite states. We give explicit expressions for W 3 and GHZ class concurrences for general pure three-partite states and for W , GHZ, and GHZ class ...

We start with a short introduction to the roof concept. An elementary discussion of phase-damping channels shows the role of anti-linear operators in representing their concurrences. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length two, getting the induced foliations of the state space, the optimal decompositions, and the entropy of a state with r...