The Importance of the Algorithmic Information Theory to Construct a Possible Example Where NP # P - II: An Irreducible Sentence

One of the most enigmatic properties of quantum mechanics is the quantum entanglement. Since the entanglement has found very important applications in quantum communication and computing [1], new ways to determine if a quantum state is entangled or not is a crucial point. Several entanglement measures have been proposed [2-5]. Among these, the quantum relative entropy is of particular interest. It is based on the distance between the state whose entanglement one wishes to measure and the set of disentangled states. In order to calculate it, it is interesting to know the general form of an n-way disentangled state. It is obvious that, if a n-partite of qubit quantum state cannot be written in the form of a general n-partite disentangled stated, then it is entangled. For example, a bipartite state AB has 2-way entanglement if