Understanding the Adjoint of |01> in Quantum Computing

Thread starter quantumstudent
Start date Mar 12, 2023

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Mar 12, 2023

quantumstudent

Homework Statement: Is <01| the adjoint of |01>?

Relevant Equations: adjoint(|01>)

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Mar 12, 2023

malawi_glenn

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Is there a way for you to check if ## \langle 0 1 |## is the "adjoint" of ## | 0 1 \rangle##?

Mar 12, 2023

quantumstudent

There's what I did in the show my work section; I'm asking if it's correct.

1. What is the definition of the adjoint of |01>?

The adjoint of a quantum state |ψ> is defined as the complex conjugate transpose of |ψ>, denoted as |ψ>†. In the case of the state |01>, its adjoint is |01>† = (|0>†)(|1>†) = (|0>)(|1>) = |01>.

2. How is the adjoint of |01> different from the original state?

The adjoint of a quantum state is different from the original state in that it is the complex conjugate transpose of the state. This means that the adjoint may have different coefficients and may also have a different overall phase factor.

3. What is the physical significance of the adjoint of |01>?

The adjoint of a quantum state has physical significance in quantum mechanics as it is used in calculating the inner product between two states. It is also used in determining the expectation value of a quantum observable.

4. How is the adjoint of |01> related to the Hermitian conjugate?

The adjoint of a quantum state |ψ> is equivalent to the Hermitian conjugate of |ψ>, denoted as |ψ>† = |ψ>†. However, the Hermitian conjugate is often used for operators, while the adjoint is used for quantum states.

5. Can the adjoint of |01> be calculated for any quantum state?

Yes, the adjoint of any quantum state can be calculated by taking the complex conjugate transpose of the state. However, in some cases, the adjoint may be equivalent to the original state, such as for real-valued states.|01>† = |01>.