local model. The mentioned proofs about the existence of local models assume that there is only one copy of the quantum state available at a time. If the particles are allowed to perform local measurements on many copies of such states, then many apparently local states (e.g., the qubit Werner states) can no longer be described by a local model. This is, in particular, true for all distillable states. However, it remains an open question whether all entangled states become non-local given sufficiently many copies. In short, entanglement of a state shared by two particles is necessary but not sufficient for that state to be non-local. It is important to recognize that entanglement is more commonly viewed as an algebraic concept, noted for being a prerequisite to non-locality as well as to quantum teleportation and to superdense coding, whereas non-locality is defined according to experimental statistics and is much more involved with the foundations and interpretations of quantum mechanics. Quantum mechanical framework The following subsections are for those with a good working knowledge of the formal, mathematical description of quantum mechanics, including familiarity with the formalism and theoretical framework developed in the articles: bra–ket notation and mathematical formulation of quantum mechanics. Pure states Consider two arbitrary quantum systems and , with respective Hilbert spaces and . The Hilbert space of the composite system is the tensor product If the first system is in state and the second in state , the state of the composite system is States of the composite system that can be represented in this form are called separable states, or product states. Not all states are separable states (and thus product states). Fix a basis for and a basis for . The most general state in is of the form . This state is separable if there exist vectors so that yielding and It is inseparable if for any vectors at least for one pair of coordinates we have If a state is inseparable, it is called an 'entangled state'. For example, given two basis vectors of and two basis vectors of , the following is an entangled state: If the composite system is in this state, it is impossible to attribute to either system or system a definite pure state. Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state),