3. More about entanglement a) Is this 2-particle state |a) = ½ (| +)1| +)2 − | +)11 −)2 + | −)1| +)2 − 1 −)11 −)₂) entangled? (Explain why or why not.) b) Consider the state |B) = 1 +)₁| +)2 + √⁄ | +)₂1 −)₂ + ¾ | −)₁| +₂ (i) What is the probability that observer #1 measures + 2? (ii) What is the probability that BOTH observers measure + +2/? (iii) Finally, what is the probability that observers 1 and 2 get "opposite" measurements of Sz? For each of the above, explain your reasoning, don't just write down an answer.
3. More about entanglement a) Is this 2-particle state |a) = ½ (| +)1| +)2 − | +)11 −)2 + | −)1| +)2 − 1 −)11 −)₂) entangled? (Explain why or why not.) b) Consider the state |B) = 1 +)₁| +)2 + √⁄ | +)₂1 −)₂ + ¾ | −)₁| +₂ (i) What is the probability that observer #1 measures + 2? (ii) What is the probability that BOTH observers measure + +2/? (iii) Finally, what is the probability that observers 1 and 2 get "opposite" measurements of Sz? For each of the above, explain your reasoning, don't just write down an answer.
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Transcribed Image Text:**3. More about entanglement**
a) Is this 2-particle state \( |\alpha\rangle = \frac{1}{2} ( |+\rangle_1 |+\rangle_2 - |+\rangle_1 |-\rangle_2 + |-\rangle_1 |+\rangle_2 - |-\rangle_1 |-\rangle_2 ) \) entangled? (Explain why or why not.)
b) Consider the state \( |\beta\rangle = \frac{1}{\sqrt{6}} |+\rangle_1 |+\rangle_2 + \frac{1}{\sqrt{6}} |+\rangle_1 |-\rangle_2 + \frac{2}{\sqrt{6}} |-\rangle_1 |+\rangle_2 \)
(i) What is the probability that observer #1 measures \( +\frac{\hbar}{2} \)?
(ii) What is the probability that BOTH observers measure \( +\frac{\hbar}{2} \)?
(iii) Finally, what is the probability that observers 1 and 2 get “opposite” measurements of \( S_z \)?
For each of the above, explain your reasoning, don’t just write down an answer.
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