I have released a new tutorial exploring one of the most counter-intuitive results in quantum mechanics: The Quantum Pigeonhole Paradox.
Classically, the Pigeonhole Principle states that if you put three pigeons into two boxes, at least one box must contain more than one pigeon. In the quantum realm, however, using pre-selection and post-selection, we can construct a scenario where we can verify that no two particles share a box.
What this Tutorial Covers
In this Qiskit 2.x notebook, we explore:
- The Paradox Setup: Constructing the circuit for three particles and two boxes (states \(|L\rangle\) and \(|R\rangle\)).
- The Measurement Problem: Demonstrating how a standard “strong” measurement collapses the state and destroys the paradox.
- Weak Measurements: Using a weak, reversible probe (Compute \(\rightarrow R_y(\epsilon) \rightarrow\) Uncompute) to extract information without collapsing the interference pattern.
- Interference Recovery: Observing how the paradox re-emerges when we limit the disturbance to the system.
Key Insight
This paradox forces us to reconsider the nature of trajectories and correlations in quantum systems. It demonstrates that “logic” about the past (e.g., “which box were they in?”) depends heavily on the measurement strength and the post-selection choice.
This tutorial is open-source and compatible with Qiskit 2.x. You can view the full derivation and run the simulation yourself.
Citation: > Dikran Meliksetian, The Quantum Pigeonhole Paradox in Qiskit 2.x: From Strong to Weak Measurements, DOI: 10.5281/zenodo.17387139.