Level 5 · Advanced undergraduate
Objective. Predict interference after a relative phase change.
Before this lesson. L5-02
Hands-on lab. Interference
Learn¶
Two paths can contribute amplitudes to the same outcome. Add those amplitudes before taking the squared magnitude. Their relative phase controls whether they reinforce or cancel. Adding the two path probabilities instead would remove the interference term.
A phase applied to the whole state has no effect on outcome probabilities. A phase applied to only one component can change a later measurement. This distinction separates global phase from relative phase. The measurement apparatus selects which distinction is observable.
Interference is not a claim that a detector reports every path. One trial still gives one registered outcome. The circuit combines amplitudes before detection. Compare several phase settings with repeated preparation to test the resulting probability curve.
Practice¶
Solution
The cosine of 2pi/3 is -1/2. Thus P(0) is 1/4 and P(1) is 3/4. Their sum remains one. Relative phase changes the interference result.
Check your understanding¶
Which operation can reveal a relative phase?
A. A measurement in a suitable changed basis
B. Reading a global phase directly
C. Adding path probabilities before combining
Show the answer
A. A measurement in a suitable changed basis
A changed basis can turn a relative phase into unequal outcome probabilities. Global phase remains absent from every measurement probability.
Sources¶
This lesson draws on Basics of quantum information, n.d.Preskill, n.d..
Next: L5-04 · Tensor products and entanglement
- Basics of quantum information. (n.d.). https://quantum.cloud.ibm.com/learning/en/courses/basics-of-quantum-information
- Preskill, J. (n.d.). Course Information for Physics 219/Computer Science 219 Quantum Computation (Formerly Physics 229). California Institute of Technology course page with lecture notes. https://www.preskill.caltech.edu/ph219/