Probabilistic Cloning: Difference between revisions

*'''Two qubit case:''' This special case is a more practical and clear example of the above general probabilistic cloner. One is only interested in two non-orthogonal qubits to be effectively copied by the probabilistic cloning machine. Here, the orthonormal bases are <math>|0\rangle</math> and <math>|1\rangle</math>. At the first stage of the protocol, only two blank states (<math>|0\rangle|0\rangle</math>) are needed. At the second stage, the unitary transformation takes the states to a superposition of two identical states along with the state <math>|0\rangle</math> and a two-qubit state (wrong state) along with the qubit <math>|1\rangle</math>. At the final stage, the third qubit is be measured in basis <math>\{|0\rangle,|1\rangle\}</math>. If the result of the measurement is <math>|0\rangle</math> the protocol is successful. Otherwise, the round is discarded. This construction can be shown more clearly in the quantum circuit below.

* <math>S = {|\psi_1\rangle, |\psi_2\rangle, ...}:</math> Set of linearly independent states which can be copied by the probabilistic cloning machine

* <math>|\psi\rangle:</math> Input state of the probabilistic cloner