By Kenneth Lyell Pregnell; Griffith University. School of Science

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5. 4) to try and infer a message from Bob which we constrained previously to be consistent with causality. 2 Independent a priori probability We postulated in the preceding section that all faithfully recording measuring devices must, in order to preserve causality, be such that the sum of all the MDOs be proportional to the identity operator acting on the state space of the system. 4). 23) ˆ j -independent. Since this probability depends only on the PDOs as this probability is Γ describing Alice’s preparation procedure, we attribute choice to Alice and say that she can choose the probability i of an outcome.

30) ˆ ′b and the cyclic property of the trace we can rewrite this as Using the definition of Γ j Pr(k|i, j) = ˆb (t2 , t1 )Ω ˆb U ˆ† ˆb Trb [U ij b (t2 , t1 )Γk ] . 29) that Ω ij be offered to the above configuration. 6. CONDITIONAL STATE GENERATION 23 we would obtain by decomposing the entire dynamics into a single preparation event at time ˆ b and a measurement event associated with the MDO Γ ˆ b at t1 associated with the PDO Ω ij k time t2 . The preparation produces a state of the quantum subsystem b that is conditioned on the preparation outcome (i, j).

The description of the remaining subsystem is then correlated to the outcome of the measurement event. In this section we show that the remaining subsystem can indeed be described mathematically by a predictive density operator conditioned on the outcome of the measurement event. 6. CONDITIONAL STATE GENERATION 21 a PDO associated with this event. From this we then derive an expression for the a priori probability in which this conditional state is produced. What is then interesting is to consider the time reversal of this situation.

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