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How can you construct the different Bell states? For example $$\frac{|01⟩-|10⟩}{\sqrt{2}}$$

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Firstly construct following circuit:

enter image description here

Different Bell states are created according to input to the circuit follwingly:

  • input $|00\rangle$, output: $|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$
  • input $|10\rangle$, output: $|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle)$
  • input $|01\rangle$, output: $|\psi\rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)$
  • input $|11\rangle$, output: $|\psi\rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle)$
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By a combination of Hadamard Gate and CNOT Gate.

Check the links below:

https://www.quora.com/What-is-the-matrix-of-a-Hadamard-with-a-CNOT-gate

https://physics.stackexchange.com/questions/418422/negative-of-quantum-gates-and-entangled-states

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