<span title="Home" class="fa-solid-900 icon"></span> Home

Technology

Area of technology

Social technology

Education

University

Universities by country

British university

List of British universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Computer science course of the University of Oxford

Year 2 or 3 course of the computer science course of the University of Oxford

Quantum Information course of the University of Oxford

Quantum Information course of the University of Oxford Hilary 2023

Quantum Information course of the University of Oxford Hilary 2023 problem sheet

Quantum Information course of the University of Oxford Hilary 2023 problem sheet 1

{scope}

It is the <norm induced by the complex dot product> over <\C^2>:
$$
|\ket{\psi}|
= \sqrt{\left|\frac{1 + i}{2}\right|^2 + \left|\frac{1-i}{2}\right|^2}
= \sqrt{\left|\frac{1}{2} + i\frac{1}{2}\right|^2 + \left|\frac{1}{2} + i\frac{-i}{2}\right|^2}
= \sqrt{
    \sqrt{\left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^2}^2 +
    \sqrt{\left(\frac{1}{2}\right)^2 + \left(\frac{-1}{2}\right)^2}^2
  }
= \sqrt{
    \left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^2 +
    \left(\frac{1}{2}\right)^2 + \left(\frac{-1}{2}\right)^2
  }
= \sqrt{\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4}} +
= \sqrt{\frac{1 + 1 + 1 + 1}{4}}
= 1
$$


a

 Ancestors (19)

Discussion (0)

Articles by others on the same topic (0)

a

 Ancestors (19)

Discussion (0) Subscribe (1)

Articles by others on the same topic (0)

Discussion (0)