Abstract Bohr’s complementarity principle has been challenged by quantum delayed-choice experiments wherein quantum systems are claimed to behave neither as wave nor as a particle, but in an intermediary way. However, this conclusion has been supported by retro-inference and with no direct link with the system quantum state. Here, we consider a framework that employs an operational criterion of physical reality to diagnosis the system ontology directly from the quantum state at each instant of time. We show that, in disparity with previous proposals, our setup ensures a formal link between the output visibility and elements of reality within the interferometer. An experimental proof-of-principle is provided for a two-spin-1/2 system in an interferometric setup implemented in a nuclear magnetic resonance platform. We discuss how our results validate, to a great extent, Bohr’s original formulation of the complementarity principle and unveil morphing reality states.
Abstract Bohr’s complementarity principle has been challenged by quantum delayed-choice experiments wherein quantum systems are claimed to behave neither as wave nor as a particle, but in an intermediary way. However, this conclusion has been supported by retro-inference and with no direct link with the system quantum state. Here, we consider a framework that employs an operational criterion of physical reality to diagnosis the system ontology directly from the quantum state at each instant of time. We show that, in disparity with previous proposals, our setup ensures a formal link between the output visibility and elements of reality within the interferometer. An experimental proof-of-principle is provided for a two-spin-1/2 system in an interferometric setup implemented in a nuclear magnetic resonance platform. We discuss how our results validate, to a great extent, Bohr’s original formulation of the complementarity principle and unveil morphing reality states.
Delayed-choice experiments challenge classical intuitions by allowing the configuration of an interferometer to be chosen after a quantum system has already entered it. While these experiments support Bohr’s complementarity principle, the introduction of quantum control reveals that the manifestation of complementarity depends critically on the full physical context — including quantum correlations and the causal order of operations. In this work, we propose and analyze a modified entanglement-assisted delayed-choice experiment that maintains the same final visibility as the standard setup but reverses its causal structure. Here, we go beyond output statistics to examine how wave-particle realism evolves throughout the interferometer. Using a contextual realism quantifier, we show that wave and particle realism can be meaningfully assigned at intermediate stages with a clear connection with the final interferometric visibility. Specifically, our results show that modifying the causal order of operations and information structure, whether through entanglement tuning or post-selection, leads to significant variations in the wave-particle complementarity relation.
Abstract Quantum delayed-choice experiments are designed to probe the robustness of the complementarity principle. In this proceeding, we revisit the main ideas reported recently in Ref. [Commun. Phys. 5, 82 (2022)] concerning a setup (quantum-controlled reality experiment) that has the same final visibility as the quantum version of Wheeler’s delayed-choice arrangement. Besides the same final statistics, upon an operational criterion of physical realism, the authors claimed a different state of affairs for the wave-and-particle behavior in delayed-choice experiments. To this end, we put forward an analysis by employing the relative entropy of coherence to study how the local wave and particle coherences when the system is traveling inside the interferometer change accordingly to the final observed visibility.
Recently, Bohr's complementarity principle was assessed in setups involving delayed choices. These works argued in favor of a reformulation of the aforementioned principle so as to account for situations in which a quantum system would simultaneously behave as wave and particle. Here we defend a framework that, supported by well-known experimental results and consistent with the decoherence paradigm, allows us to interpret complementarity in terms of correlations between the system and an {\em informer}. Our proposal offers formal definition and operational interpretation for the dual behavior in terms of both nonlocal resources and the couple work-information. Most importantly, our results provide a generalized information-based trade-off for the wave-particle duality and a causal interpretation for delayed-choice experiments.
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).
Gedanken experiments are important conceptual tools in the quest to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behaviour of the controlling devices in such experiments. We propose a framework to analyse quantum-controlled experiments and illustrate the implications by discussing a quantum version of Wheeler's delayed-choice experiment. The introduction of a quantum-controlled device (i.e., quantum beamsplitter) has several consequences. First, it implies that we can measure complementary phenomena with a single experimental setup, thus pointing to a redefinition of complementarity principle. Second, a quantum control allows us to prove there are no consistent hidden-variable theories in which particle and wave are realistic properties. Finally, it shows that a photon can have a morphing behaviour between particle and wave; this further supports the conclusion that particle and wave are not realistic properties but merely reflect how we 'look' at the photon. The framework developed here can be extended to other experiments, particularly to Bell-inequality tests.
Bohr's complementarity notion is at the heart of quantum physics, and suggests that in a quantum experiment, the observed phenomena are inherently linked to the type of measurement that is performed. For example, sending single photons to an open or closed Mach-Zehnder interferometer leads to the observation of particle or wave behaviours. In 1984, Wheeler proposed a 'Gedanken' experiment in which the experimentalist chooses the interferometer configuration, at will, only after the photon has already passed the input beam-splitter (BSin) of the device. This experiment was realized using a diamond-based single photon source, and it was shown that Bohr's complementarity notion was still obeyed, as expected. It was recently proposed theoretically to take Wheeler's experiment one step further by employing a 'quantum beam-splitter' (QBS) at the interferometer output. In this case, the output beam-splitter (BSout) is placed in a coherent superposition of being absent and present, which also allows to further delay the choice of the measurement type. The type of measurement is determined only after having measured the state of the QBS, which can be (in principle) infinitely delayed. We demonstrate the realization of such an experiment by exploiting entanglement. In particular, we take advantage of pairs of polarization entangled photons. The behaviour of one of the paired photons, called the test photon, is analysed by sending it to a Mach-Zehnder interferometer having an entanglement-enabled QBS at its output. This device is made of a polarization dependent beam-splitter followed by polarization state erasers. The other photon, called the corroborative photon, allows determining the actual state of the QBS, and consequently, which test photon behaviour (wave, particle, or both) is measured. By manipulating the corroborative photon, we demonstrate a continuous morphing from wave to particle behaviour, which refutes too simple views of single photons behaving exclusively as waves or particles. The measurements on the test photon and the interferometer configuration are performed in a strictly delayed manner. The state of the QBS is measured only after the test photon already left the interferometer, and is detected, which means that it is destroyed before the type of measurement it under- goes is determined. We find that even in this configuration, Bohr's complementarity notion, and its extension, are perfectly obeyed. The space-like separation between the measurements invalidates local-hidden variable models associated with pre-existing information about the measurement out- comes. In other words, when the test photon is detected, no information is available about the type of measurement that was performed. This assertion is confirmed by the violation of the Bell's inequalities with more than 10 standard deviations. The presence of entanglement shows furthermore that genuine quantum behaviour for the test photons has been observed. As a conclusion, we have demonstrated the experimental realization of the quantum version of Wheeler's experiment. Trying to explain our observations in classical terms causes severe contradictions, but the results are in perfect agreement with quantum physics, in which the measurement timing order does not matter. The beauty in such experiments is that space and time do not seem to play any role.