is one of the famous “Bell states,” a highly entangled state of its two qubits. In this qu...

is one of the famous “Bell states,” a highly entangled state of its two qubits. In this question we examine some of its strange properties.

(a) Suppose this Bell state could be decomposed as the (tensor) product of two qubits (recall the box on page 300), the first in state α0|0〉+α1|1〉  and the second in state β0|0〉+β1|1〉.Write four equations that the amplitudes β0, β1, β0, and β1 must satisfy. Conclude that the Bell state cannot be so decomposed.

(b) What is the result of measuring the first qubit of |ψ〉?

(c) What is the result of measuring the second qubit after measuring the first qubit?

(d) If the two qubits in state |ψ〉are very far from each other, can you see why the answer to (c) is surprising?