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State Dependent N-M Cloning: Difference between revisions
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* State-dependent cloning machine only transforms a set of two non-orthogonal input states, parametrized as follows: | * State-dependent cloning machine only transforms a set of two non-orthogonal input states, parametrized as follows: | ||
<math>|a\rangle = cos\theta |0\rangle + sin\theta |1\rangle,</math></br> | <math>|a\rangle = cos\theta |0\rangle + sin\theta |1\rangle,</math></br> | ||
|b\rangle = sin\theta |0\rangle + cos\theta |1\rangle,</math></br> | <math>|b\rangle = sin\theta |0\rangle + cos\theta |1\rangle,</math></br> | ||
where <math>\theta \in [0, \pi/4]</math> and their scalar product (or inner product) is specified as <math>S = \langle a|b \rangle = sin 2\theta</math>. | where <math>\theta \in [0, \pi/4]</math> and their scalar product (or inner product) is specified as <math>S = \langle a|b \rangle = sin 2\theta</math>. | ||
* The condition that transformation should be unitary adds following constraint on the scalar product of final states:</br> | * The condition that transformation should be unitary adds following constraint on the scalar product of final states:</br> | ||
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where the reduced density matrix of the subsystem <math>a</math> (The quantum state of a subsystem in density matrix representation) is described as:</br> | where the reduced density matrix of the subsystem <math>a</math> (The quantum state of a subsystem in density matrix representation) is described as:</br> | ||
<math>\rho_{\alpha} = (A+B)^2 |a\rangle\langle a| + (A-B)^2 |b\rangle\langle b| + (A^2 - B^2)S^{M-1}(|a\rangle\langle b| + |b\rangle\langle a|)</math></br> | <math>\rho_{\alpha} = (A+B)^2 |a\rangle\langle a| + (A-B)^2 |b\rangle\langle b| + (A^2 - B^2)S^{M-1}(|a\rangle\langle b| + |b\rangle\langle a|)</math></br> | ||
A and B are presented in the [[ | A and B are presented in the [[State Dependent N-M Cloning#Pseudo Code|Pseudo Code]] section. | ||
==Pseudo Code== | ==Pseudo Code== | ||
'''General Case''' | '''General Case''' | ||