Proposal for a Quantum Delayed-Choice Experiment

Gedanken experiments help to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behavior of the controlling devices in such experiments. We propose a framework to analyze quantum-controlled experiments and illustrate it by discussing a quantum version of Wheeler’s delayed-choice experiment. Using a quantum control has several consequences. First, it enables us to measure complementary phenomena with a single experimental setup, pointing to a redefinition of complementarity principle. Second, it allows us to prove there are no consistent hidden-variable theories having “particle” and “wave” as realistic properties. Finally, it shows that a photon can have a morphing behavior between particle and wave. The framework can be extended to other experiments (e.g., Bell inequality).

Figure 1

(a) In the classical delayed-choice experiment the second beam splitter is inserted or removed randomly after the photon is already inside the interferometer. (b) The equivalent quantum network. An ancilla (red line), initially prepared in the state $|+⟩=\frac{1}{\sqrt{2}}(|0⟩+|1⟩)$ then measured, acts as a quantum random number generator (QRNG). (c) Delayed choice with a quantum beam splitter. The classical control (red double line) after the measurement of the ancilla in (b) is equivalent to a quantum control before the measurement; the second beam splitter ${\mathrm{BS}}_2$ is now in superposition of present and absent, equivalent to a controlled-Hadamard $C(H)$ gate. (d) We bias the QRNG by preparing the ancilla in an arbitrary state $\cos \alpha |0⟩+\sin \alpha |1⟩$.

Figure 2

Morphing behavior between particle ($\alpha =0$) and wave ($\alpha =\pi /2$).