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Modern science has produced few stories as strange as the behaviour of light. In the everyday world we treat objects as either particles moving along definite trajectories or, waves spreading through space. But light - photons - refuse to pick a side. In the early 20th century, experiments like the legendary double-slit produced interference patterns even when single photons were sent through two apertures, and yet those same photons impacted the screen one at a time as though they were tiny bullets. It’s like shooting an arrow and the trajectory of the arrow bends and curves without any external forces. Such wave-particle duality is not a metaphor; it’s real and you can literally prove it yourself at home.

Now, please allow me to drag you into the world of weirdness. Consider a Mach-Zehnder interferometer. A photon enters a beam-splitter and has two possible paths. If the interferometer is complete (there is a beam-splitter at the end), interference fringes appear because the photon behaves like a wave that travels both paths simultaneously. If the second beam-splitter is removed, the photon shows particle-like behaviour and the detectors click with equal probability. In the experiment described by Rab and colleagues, the authors label these output states “|w)” for wave and “|p)” for particle. They find that the probability of detecting the photon in the wave channels depend on the interferometer’s phase, showing that the photon took both paths, while the particle channels show no interference and behave as if the photon chose a single path. This ability to morph continuously between wave and particle-like behaviours by adjusting experimental parameters is a hallmark of quantum physics.

From a classical point of view, an object cannot simultaneously travel along two mutually exclusive paths. It is also tempting to imagine that photons have hidden instructions telling them how to behave, but the delayed-choice experiments of Wheeler allow researchers to decide whether to observe wave or particle behaviour after the photon has entered the interferometer. Such experiments rule out the idea that the photon carried hidden information about how to behave. Even more strikingly, recent quantum delayed-choice experiments show that a single photon can display both wave- and particle-like behaviour at the same time. And thus the definitions of “wave” and “particle” have therefore become operational, i.e., “wave-like” means capable of producing interference while “particle-like” means incapable of producing interference.

Niels Bohr summarised the situation with his principle of complementarity. Certain properties such as which path a photon took and whether it interfered cannot be simultaneously well-defined. Andrea Aiello elaborates on this idea by introducing a new continuous-discrete duality. He argues that the weird aspect of wave-particle duality is not just about paths and interference patterns, but about the very nature of measurement itself. In an arXiv study accepted by Quantum journal, Aiello notes that the simultaneous measurement of a beam’s wave amplitude and its photon number is prohibited by quantum mechanics. Classical physics would have no issue measuring the amplitude of a light wave and the number of quanta separately. In quantum theory, however, these are complementary observables; the more precisely one knows the photon number, the less meaningfully one can assign a well-defined continuous amplitude. Classical waves have amplitudes that vary smoothly, and classical particles have integer counts. Photons, by contrast, exhibit both behaviours only probabilistically, and the formalism of quantum field theory shows that these aspects cannot be simultaneously realised.

Getting even weirder

When we extend the superposition principle to systems of more than one particle, we encounter what’s called as, “entanglement.” Instead of independent wavefunctions for each particle, their degrees of freedom become inseparable, like two masses connected by a spring. The Nature Communications study on “Entanglement of photons in their dual wave-particle nature” notes that entanglement “gathers fundamental quantum correlations among particle properties,” and these correlations are “at the core of non-locality” and essential for developing quantum technologies. These correlations cannot be explained by any classical theory that assigns predefined values to each particle.

The same experiment shows that entanglement can exist between wave and particle-like degrees of freedom themselves. The researchers first generate single-photon states that are superpositions of the |w) and |p) models. By duplicating this setup for two photons and injecting each photon a polarisation-entangled pair into an independent “wave-particle toolbox,” they create entangled states where the wave or particle behaviour of one photon is correlated with that of the other. In classical optics, one might imagine correlating two beams’ intensities or phases, but here the correlation involves whether each photon takes one path or two, an intrinsically quantum property.

The experiment scheme also reveals how interference emerges only when the |w) and |p) components can interfere in the detection stage. If the experimenter chooses settings that erase this interference, the photon behaves like a classical mixture and the interference term vanishes. When the interference is allowed, the probability of detection depends on the phase difference and reveals the wave-like behaviour. Such control over wave-particle superposition and entanglement suggests that quantum properties are again, contextual, not inherent features carried by the photon from the source but properties that emerge from the interaction between the photon and the apparatus. So weird!

In today’s world, quantum entanglement is more than just a philosophical curiousity; it is the fuel powering the emerging quantum economy. Quantum key distribution schemes use entangled photon pairs to guarantee secure communication. Quantum computers harness entanglement among qubits to perform computations that would be infeasible on classical machines. Quantum sensors exploit entangled states to measure physical quantities with precision beyond classical limits. And quantum physics...continues to challenge our intuitions about reality.

For the love of mankind,

Krish

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