Measurement Probability (|0⟩) Calculator
Probability of measuring |0⟩ from amplitude α.
Formula first
Overview
This equation represents the application of Born's Rule to a single qubit, defining the relationship between a state's probability amplitude and its observable outcome. It quantifies the likelihood that a quantum system in a superposition will collapse into the specific basis state |0⟩ upon measurement.
Symbols
Variables
P_0 = P(|0⟩), \alpha = α
Apply it well
When To Use
When to use: Apply this formula when you need to predict the measurement statistics of a qubit whose state vector is defined in the computational basis. It assumes the system is undergoing a projective measurement and that the state vector is properly normalized.
Why it matters: This principle is the fundamental link between the linear algebra of quantum mechanics and the probabilistic results of physical experiments. It allows developers to design quantum algorithms by manipulating amplitudes to maximize the probability of measuring the correct answer.
Avoid these traps
Common Mistakes
- Using |α| instead of |α|² for the probability.
- Forgetting to check that the state is normalised before applying Born's Rule.
One free problem
Practice Problem
A qubit is prepared in a superposition where the amplitude of the ground state alpha is 0.6. Calculate the probability P0 that the qubit will be measured in the |0⟩ state.
Solve for:
Hint: Square the magnitude of the amplitude alpha to find the probability.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information
- David J. Griffiths, Darrell F. Schroeter, Introduction to Quantum Mechanics
- Wikipedia: Born rule
- Griffiths, David J. Introduction to Quantum Mechanics
- Nielsen, Michael A., and Chuang, Isaac L. Quantum Computation and Quantum Information
- Nielsen and Chuang Quantum Computation and Quantum Information
- Griffiths Introduction to Quantum Mechanics
- IUPAC Gold Book