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29 to environment, or an eavesdropper, or any other reason), and we can calculate the obtained state, the error rate is pe = 1 − ψ 1 |ρ|ψ 1 . 30) The definition of a quantum memory contains more that just the ability to preserve a quantum state for a long time. Other necessary conditions are the input / output abilities: One must be able to produce a known quantum state; One must be able to input an unknown state into the memory; One must be able to measure the state in some well defined basis, or furthermore, to take it out of the memory (without measuring it) in order to perform any unitary transformation on it (alone, or together with other particles).

In the OT protocols a cheating Alice would like to control the probability that Bob receive the bit in OT or to learn whether Bob got the bit or not, and a cheating Bob would like to learn the bit with probability better than 50%. The two versions of OT are equivalent[32]: OT is derived from 21 OT by considering only one bit of the two. A protocol for 21 OT is derived from OT as follows: Alice and Bob perform OT several times. Bob arranges the bits in two strings — a string of bits he knows and a string of bits he doesn’t; He tells Alice the groups but not which group is known to him.

If the channel is very lossy, Eve could take advantage of it and learn all information: she performs the optimal deterministic attack, and throws away the bits whenever she got an inconclusive result. Thus, in order to use this scheme we must restrict also the losses in addition to the restriction on the error rate, or alternatively use a reference signal [4]. To simplify further discussion of this scheme we redefine Pe to include the losses, thus it is better for Eve to send something (which might not be counted as error) than to keep the particle.