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Asymmetric Universal 1-2 Cloning: Difference between revisions
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<math>F_a = 1 - \frac{b^2}{2}, F_b = 1 - \frac{a^2}{2}</math> | <math>F_a = 1 - \frac{b^2}{2}, F_b = 1 - \frac{a^2}{2}</math> | ||
== | ==Protocol Description== | ||
===General Case=== | ===General Case=== | ||
For more generality, we use the [[density matrix]] representation of the states which includes [[mixed states]] as well as [[pure states]]. For a simple pure state <math>|\psi\rangle</math> the density matrix representation will be <math>\rho_{\psi} = |\psi\rangle\langle\psi|</math>. Let us assume the initial qubit to be in an unknown state <math>\rho_{\psi}</math>. Our task is to clone this qubit universally, i.e. input-state independently, in such a way, that we can control the scaling of the original and the clone at the output. In other words, we look for output which can be represented as below:</br> | For more generality, we use the [[density matrix]] representation of the states which includes [[mixed states]] as well as [[pure states]]. For a simple pure state <math>|\psi\rangle</math> the density matrix representation will be <math>\rho_{\psi} = |\psi\rangle\langle\psi|</math>. Let us assume the initial qubit to be in an unknown state <math>\rho_{\psi}</math>. Our task is to clone this qubit universally, i.e. input-state independently, in such a way, that we can control the scaling of the original and the clone at the output. In other words, we look for output which can be represented as below:</br> | ||