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Showing Show that a matrix$\lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$ is the Choi–Jamiołkowski matrix of a quantum channel

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mikanim
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I'm curious how to show how this matrix:

$$c = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$

is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$

Edit: Additional question: What is the Klaus representation (operator-sum representation) of the quantum channel T that is described by c and show that $T_{1/2}$ is an entanglement breaking quantum channel and describe its action on the bloch sphere.

I'm curious how to show how this matrix:

$$c = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$

is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$

Edit: Additional question: What is the Klaus representation (operator-sum representation) of the quantum channel T that is described by c and show that $T_{1/2}$ is an entanglement breaking quantum channel and describe its action on the bloch sphere.

I'm curious how to show how this matrix:

$$c = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$

is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$

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mikanim
  • 297
  • 1
  • 6

I'm curious how to show how this matrix:

$$c = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$

is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$

Edit: Additional question: What is the Klaus representation (operator-sum representation) of the quantum channel T that is described by c and show that $T_{1/2}$ is an entanglement breaking quantum channel and describe its action on the bloch sphere.

I'm curious how to show how this matrix:

$$c = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$

is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$

I'm curious how to show how this matrix:

$$c = \lambda |\phi^+\rangle \langle\phi^+| + (1-\lambda )|\phi^-\rangle \langle\phi^-|$$

is the Choi–Jamiołkowski matrix of a quantum channel for any $\lambda \in [0,1]$

Edit: Additional question: What is the Klaus representation (operator-sum representation) of the quantum channel T that is described by c and show that $T_{1/2}$ is an entanglement breaking quantum channel and describe its action on the bloch sphere.

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glS
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glS
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