The tensor product of this state is then,  Now, omitting all terms formula_37 which are not part of any sequence which is likely to occur with high probability, known as the typical set :formula_38 the new state is  And renormalizing,  Then the fidelity  Suppose that Alice and Bob are in possession of m copies of formula_9. Alice can perform a measurement onto the typical set formula_44 subset of formula_45, converting the state formula_46 with high fidelity. The theorem of typical sequences then shows us that formula_47 is the probability that the given sequence is part of the typical set, and may be made arbitrarily close to 1 for sufficiently large m, and therefore the Schmidt coefficients of the renormalized Bell state formula_48 will be at most a factor formula_49 larger. Alice and Bob can now obtain a smaller set of n Bell states by performing LOCC on the state formula_48 with which they can overcome the noise of a quantum channel to communicate successfully. Many techniques have been developed for doing entanglement distillation for mixed states, giving a lower bounds on the value of the distillable entanglement formula_51 for specific classes of states formula_13. One common method involves Alice not using the noisy channel to transmit source states directly but instead preparing a large number of Bell states, sending half of each Bell pair to Bob. The result from transmission through the noisy channel is to create the mixed entangled state formula_13, so that Alice and Bob end up sharing formula_54 copies of formula_13. Alice and Bob then perform entanglement distillation, producing formula_56 almost perfectly entangled states from the mixed entangled states formula_13 by performing local unitary operations and measurements on the shared entangled pairs, coordinating their actions through classical messages, and sacrificing some of the entangled pairs to increase the purity of the remaining ones. Alice can now prepare an formula_56 qubit state and teleport it to Bob using the formula_56 Bell pairs which they share with high fidelity. What Alice and Bob have then effectively accomplished is having simulated a noiseless quantum channel using a noisy one, with the aid of local actions and classical communication. Let formula_60 be a general mixed state of two spin-1/2 particles which could have resulted from the transmission of an initially pure singlet state  through a noisy channel between Alice and Bob, which will be used to distill some pure entanglement. The fidelity of M  is a convenient expression of its purity relative to a perfect singlet.