Question

What is the inner product of 13√|0⟩+2√3√|1⟩ and |+⟩?

Rewrite 13√|0⟩+2√3√|1⟩ in the sign basis.

Answer 1

THE #1ST

(1+sqrt(2))/sqrt(6)

Answer 2

that's wrong

Answer 3

[AI-generated answer — Explain Bot]

To find the inner product between two vectors, we need to rewrite them in the same basis. In this case, we need to rewrite the vector 13√|0⟩+2√3√|1⟩ in the sign basis.

In the sign basis, the two states |0⟩ and |1⟩ are represented by the vectors |+⟩ and |-⟩, respectively.

To rewrite the vector 13√|0⟩+2√3√|1⟩ in the sign basis, we can use the following relations:
|0⟩ = 1/√2 (|+⟩ + |-⟩)
|1⟩ = 1/√2 (|+⟩ - |-⟩)

Substituting these relations into the original vector, we get:
13√|0⟩+2√3√|1⟩ = 13√(1/√2)(|+⟩ + |-⟩) + 2√3√(1/√2)(|+⟩ - |-⟩)
= (13/√2)(√|+⟩ + √|-⟩) + (√3√/√2)(√|+⟩ - √|-⟩)
= (13/√2)√(|+⟩ + |-⟩) + (√3√/√2)√(|+⟩ - |-⟩)

Thus, the vector 13√|0⟩+2√3√|1⟩ in the sign basis is (13/√2)√(|+⟩ + |-⟩) + (√3√/√2)√(|+⟩ - |-⟩).