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| ==Properties== | | ==Properties== |
| *The protocol assumes that the original input qubit is unknown and the protocol is independent of the original input state (universality).
| | The protocol |
| *The output copies are not identical and we are able to control the likelihood (fidelity) of the output copies to the original state by pre-preparing the ancillary states with special coefficients. | | * involves two parties and one-way communication from the prover to the verifier. |
| *Claims for General case: | | * assumes that anyone might be dishonest and still provide perfect completeness and constant soundness. |
| **Following inequality holds between the scaling factors <math>s_0</math> and <math>s_1</math></br>
| | * has a communication complexity of <math>O(\sqrt{N}\log_2N)</math> bits of information. |
| <math>s_0^2 + s_1^2 + s_0 s_1 - s_0 - s_1 \leq 0</math>
| | * runs in exponential time, while it can be shown that by using classical proofs, the best protocol run in exponential time in the size of N. |
| **This elliptic inequality shows the possible value of the scaling parameters.
| | * can be implemented with linear optics (not exclusively). |
| **Trade-off inequality between the fidelities of the clones:</br> | | * It has been theorized that N needs to be at least about 500 in order to have the advantage over the best classical protocol. |
| <math>\sqrt{(1 - F_a)(1 - F_b)} \geq \frac{1}{2} - (1 - F_a) - (1 - F_b)</math> | |
| **Optimality is provided when the fidelities of two clones, <math>F_a</math> and <math>F_b</math>, saturate the above inequality | |
| *Claims for Special case with bell state: | |
| **Following ellipse equation holds between the scaling factors <math>a</math> and <math>b</math></br> | |
| <math>a^2 + b^2 + ab = 1</math>
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| **Following equations holds for fidelities of the clones:
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| <math>F_a = 1 - \frac{b^2}{2}, F_b = 1 - \frac{a^2}{2}</math>
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| ==Pseudo Code== | | ==Pseudo Code== |