You are going to analyze a protocol called entanglement swapping, which is related to quantum teleportation....

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You are going to analyze a protocol called entanglement swapping, which is related to quantum teleportation. In this protocol there are THREE parties, Alice, Bob and Cara. Alice has one qubit (which we label A), Bob has two qubits (B1 and B2), and Cara has one qubit (which we label C). The two qubits A and B1 are in a maximally entangled state |+) = (1/2)(100) + |11)), and so are the two qubits B2 and C, so the state is (10000) + |0011) + |1100) + |1111)). |Y) = |+)AB |+)BC 1 = 2 In the expression above, the first qubit is A, the second and third qubits are B1 and B2, and the fourth qubit is C. We say that Bob shares an EPR pair with Alice and shares another EPR pair with Cara. a. Bob has entanglement with Alice, and Bob has entanglement with Cara. Do you think Alice and Cara have entanglement with each other? Why or why not? b. Rewrite the state (Y) by writing Bob's two qubits (B1 and B2) in the Bell basis, while leaving Alice and Cara's qubits in the standard (Z) basis. C. If Bob measures his two qubits in the Bell basis, what are the probabilities of the four possible outcomes? d. Suppose Bob has measured his two qubits in the Bell basis and gotten the result |+). What is the state of Alice and Cara's two qubits? Are they entangled? You are going to analyze a protocol called entanglement swapping, which is related to quantum teleportation. In this protocol there are THREE parties, Alice, Bob and Cara. Alice has one qubit (which we label A), Bob has two qubits (B1 and B2), and Cara has one qubit (which we label C). The two qubits A and B1 are in a maximally entangled state |+) = (1/2)(100) + |11)), and so are the two qubits B2 and C, so the state is (10000) + |0011) + |1100) + |1111)). |Y) = |+)AB |+)BC 1 = 2 In the expression above, the first qubit is A, the second and third qubits are B1 and B2, and the fourth qubit is C. We say that Bob shares an EPR pair with Alice and shares another EPR pair with Cara. a. Bob has entanglement with Alice, and Bob has entanglement with Cara. Do you think Alice and Cara have entanglement with each other? Why or why not? b. Rewrite the state (Y) by writing Bob's two qubits (B1 and B2) in the Bell basis, while leaving Alice and Cara's qubits in the standard (Z) basis. C. If Bob measures his two qubits in the Bell basis, what are the probabilities of the four possible outcomes? d. Suppose Bob has measured his two qubits in the Bell basis and gotten the result |+). What is the state of Alice and Cara's two qubits? Are they entangled?

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a No Alice and Cara do not have entanglement with each other Entanglement is a quantum phenomenon wh... View the full answer