(a) (15 points) Recall the Bell state |01) - |10) 2 Show that ) is fixed...

Transcribed Image Text:

(a) (15 points) Recall the Bell state |01) - |10) √2 Show that ) is fixed by any operator of the form UU, where U is a 1-qubit unitary operator with determinant ±1. That is, (UU)|¥¯) = |¥¯). ) is known as the singlet state or a spin singlet. The innermost electron shell in all atoms starting with Helium are in this state. [Hint: By the Euler angle decomposition, you only need to show the identity for U = R₂ (0) and U = Ry(0) (for real #).] (b) (10 points extra credit) Show that one can get from one to any other of the three Bell states ), Þ), and +) by applying operators of the form UU, for 1-qubit unitary operators U. These states are called triplet states. Activate Windows Go to Settings to activate Windows. (a) (15 points) Recall the Bell state |01) - |10) √2 Show that ) is fixed by any operator of the form UU, where U is a 1-qubit unitary operator with determinant ±1. That is, (UU)|¥¯) = |¥¯). ) is known as the singlet state or a spin singlet. The innermost electron shell in all atoms starting with Helium are in this state. [Hint: By the Euler angle decomposition, you only need to show the identity for U = R₂ (0) and U = Ry(0) (for real #).] (b) (10 points extra credit) Show that one can get from one to any other of the three Bell states ), Þ), and +) by applying operators of the form UU, for 1-qubit unitary operators U. These states are called triplet states. Activate Windows Go to Settings to activate Windows.