Final answer:
To project a Bell state onto its new eigenbasis, we first need to understand the concept of a Bell state. We can then find the eigenbasis of the measurement operator we want to use, such as the Pauli-X operator.
Step-by-step explanation:
When it comes to projecting a Bell state onto its new eigenbasis, we first need to understand the concept of a Bell state. A Bell state is an entangled state of two qubits that are in a superposition of two basis states. To project a Bell state onto its new eigenbasis, we need to find the eigenbasis of the new measurement operator that we want to use.
For example, if we want to use the Pauli-X operator as our measurement, we can find its eigenbasis by finding the eigenvectors of the Pauli-X matrix. Once we have the eigenbasis, we can project the Bell state onto it by finding the inner product between the Bell state and each eigenvector.
This will give us the probability amplitudes of the Bell state collapsing into each eigenstate. Finally, we can measure the Bell state by performing a measurement in the eigenbasis and obtaining one of the eigenstates with their corresponding probabilities.