Quantum retrodiction

Summary form only given. Quantum mechanics is normally used predictively. In the Schrodinger picture an initially prepared state evolves according to some Hamiltonian, and when a measurement is made it is possible to predict the likelihood of obtaining a particular result. This way of looking at things does not apply well to all experimental situations. If one has no idea what state was prepared, retrodiction from a measurement of the final state provides the only information about the premeasurement state. A simple example is quantum cryptography, where Alice sends quantum states, chosen at random from a known set, to Bob in order to establish a secret key. Alice knows the state which she sent to Bob, and can predict the probabilities of particular outcomes for any measurement which Bob performs. Before the pair compare their results Bob does not know what state Alice sent. He simply chooses what to measure, and his results can be used to retrodict the probability that Alice sent particular states.