Physicists have demonstrated that quantum computers can crack a problem that is fundamentally impossible for classical systems — and the solution relies on a phenomenon Albert Einstein once dismissed as “spooky action at a distance.”
Researchers from the Autonomous University of Barcelona and Hunter College of CUNY showed that quantum entanglement can substitute for physical labels when determining whether rearranging a set of particles requires an even or odd number of swaps.
Classical systems cannot perform this task unless every particle is marked with a unique identifier. With four particles, four distinct labels are needed. But qubits — the quantum equivalent of computer bits — can only hold two perfectly distinguishable labels.
By starting particles in an entangled state, the researchers found the parity of permutations could be detected without the full labelling that classical physics demands.
Co-senior author Emili Bagan said the most striking aspect was the simplicity of the demonstration. Merely permuting particles and asking a basic yes-or-no question was enough to reveal a clear quantum advantage.
The team used representation theory from mathematics to analyse how symmetry behaves in quantum systems.
Co-senior author Mark Hillery explained the concept using an analogy of two players rearranging balls. Classically, each ball must have a unique colour to determine whether the rearrangement was even or odd. Quantum entanglement removes that requirement.
The findings, published in Physical Review Letters, could inform the development of task-specific quantum algorithms.
The researchers are now investigating broader scenarios involving different symmetry groups and questions beyond simple binary outcomes.
