Abstract
This paper proposes a quantum setup violating the pigeonhole principle. It describes how the counterfactual reasoning of the paradox may be operationally grounded in the analysis of the tiny footprints left in the environment by the pigeons. Identifying the drawbacks of recent experiments of the quantum pigeonhole effect, the authors argue that a definitive experimental violation of the pigeonhole principle is still needed and propose an implementation using modern quantum computing hardware.
Highlights
Quantum paradoxes describe phenomena that would be impossible if nature strictly obeyed classical physics
To demonstrate a quantum violation of the classical pigeonhole principle, one prepares a particular superposition of N pigeons distributed into M holes, later measures another particular superposition of the N pigeons
We will show for quantum mechanics that given a particular preand postselection scenario, we can infer with certainty that we will not find more than one pigeon in a single hole that we check
Summary
Quantum paradoxes describe phenomena that would be impossible if nature strictly obeyed classical physics. A more recent example is the quantum pigeonhole paradox [3,4] where one places a number of particles into a smaller number of boxes and infers that no two particles had occupied the same box. This latter paradox has prompted extensive discussion and several experimental implementations [5,6,7,8,9].
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