Quantum communication is possible with pure state

It is believed that quantum communication is not possible with a pure ensemble of states because quantum entropy of pure state is zero. This is indeed possible due to geometric consequence of entanglement. Quantum entropy is the measure of information content of quantum state [1,2]. Only for mixed state quantum entropy is non-zero. Therefore, one may conclude that same pure ensemble cannot be used to represent bit 0 and 1. We shall see that same pure ensemble can represent bit 0 and 1 due to entanglement. Suppose there is stock of EPR pairs. EPR pairs can be arranged in two different ways to represent bit 0 and 1. Let the two non-overlapping arrangements be S1 = {A, B, B, C, D, A, E, F, E, F, C, D,......} S0 = {B, A, D, C, D, A, E, E, F, F, B, C,......} Here the same pair of letters denote an EPR pair, say singlet state of spin 1/2 particles. So, EPR state can be described as, ( ) j i j i j i, 2 1 Ψ ↑ ↓ − ↓ ↑ = where i and j (i ≠j) denote the position of a pair in the sequence and “↑ ” and “↓ ” are two opposite spin directions. S1 and S0 are non-overlapping sequences because not a single pair occupies the same position ij in S1 and S0. Suppose Alice and Bob share the sequence codes. By sending sequences Alice can send message to Bob. This is basically entanglement-based alternative quantum coding (AQC) [3]. Alice transmits S0 or S1 to Bob. After receiving the sequence Bob measures spin components of all the particles along z axis. As Bob knows the sequence codes he recovers EPR correlation corresponding to either S0 or S1 . That is, Bob recovers bit value recovering EPR correlation. EPR pair gives any one of the two sets of data, “↑ ↓ ” and “↓ ↑ ” with equal probability. Non-EPR pair gives any one of the four sets of data , “↑ ↓ ” , “↓ ↑ ” , “ ” and “ ” with equal probability. Note that non-EPR pair also yields EPR data with probability 1/2. ↑ ↑ ↓ ↓