Phase Co-variant Cloning: Difference between revisions

*<math>|\psi(\phi)\rangle = \frac{1}{\sqrt{2}} (|0\rangle + e^{i\phi}|1\rangle):</math> Input equatorial state

*<math>T:</math> The general map for all the phase-covariant QCMs

*<math>\eta:</math> The shrinking factor, showing how the density matrix of the copies has been changed after the cloning process

*<math>U_{pc}:</math> The unitary transformation of the phase-covariant QCM without ancilla

*<math>U_{pca}:</math> The unitary transformation of the phase-covariant QCM with ancilla

*<math>\rho_A, \rho_B:</math> The reduced density matrix describing the state of subsystem <math>A(B)</math> after the cloning process

*<math>|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle):</math> The Bell state. One of the [[maximally entangled]] states for 2 qubits

*<math>\mathbb{I}:</math> The identity operation (matrix)

*<math>\sigma_x, \sigma_y, \sigma_z:</math> [[Pauli Operators]] X,Y,Z  

*<math>F_A, F_B:</math> The fidelity of the subsystem <math>A(B)</math> showing how the first(second) copy is close to the original state. In the symmetric case, these fidelities are equal and the copies are identical.