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Phase Co-variant Cloning: Difference between revisions
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==Properties== | ==Properties== | ||
*Fidelity Claims | *Fidelity Claims | ||
#'''Fidelity of the asymmetric without ancilla case:'''</br> | #'''Fidelity of the asymmetric case without ancilla case:'''</br> | ||
<math>F_A = \frac{1}{2}(1 + cos\eta) \quad F_B = \frac{1}{2}(1 + sin\eta)</math> | <math>F_A = \frac{1}{2}(1 + cos\eta) \quad F_B = \frac{1}{2}(1 + sin\eta)</math> | ||
#'''Fidelity of the symmetric without ancilla case:''' The special case of the asymmetric phase-covariant cloning with <math>\eta = \pi/4</math>. This fidelity is larger than the fidelity of the [[Quantum Cloning|Universal QCM]]:</br> | #'''Fidelity of the symmetric case without ancilla case:''' The special case of the asymmetric phase-covariant cloning with <math>\eta = \pi/4</math>. This fidelity is larger than the fidelity of the [[Quantum Cloning|Universal QCM]]:</br> | ||
<math>F_{A,B} = \frac{1}{2}(1 + \frac{1}{\sqrt{2}}) \approx 0.8535 > \frac{5}{6}</math></br> | <math>F_{A,B} = \frac{1}{2}(1 + \frac{1}{\sqrt{2}}) \approx 0.8535 > \frac{5}{6}</math></br> | ||
#'''Fidelity of the general with ancilla case:''' The same as the without ancilla case:</br> | #'''Fidelity of the general case with ancilla case:''' The same as the without ancilla case:</br> | ||
<math>F_A = \frac{1}{2}(1 + cos\eta) \quad F_B = \frac{1}{2}(1 + sin\eta)</math> | |||
*'''Case 1 (without ancilla):''' The state of each copy which is a subsystem of this two-qubit system is described with a [[density matrix]] which can be obtained as below</br> | *'''Case 1 (without ancilla):''' The state of each copy which is a subsystem of this two-qubit system is described with a [[density matrix]] which can be obtained as below</br> | ||
<math>\rho_A = Tr_B (|\psi(\phi)_F\rangle\langle\psi(\phi)_F|)</math></br> | <math>\rho_A = Tr_B (|\psi(\phi)_F\rangle\langle\psi(\phi)_F|)</math></br> | ||