We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability tradeoff via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM superconducting transmon processor. A detailed analysis of the results is provided. Despite finding good agreement with theory at a coarse level, we also identify small but persistent systematic deviations preventing the observation of full particlelike and wavelike statistics. We understand them by carefully modeling two-qubit gates, showing that even small coherent errors in their implementation preclude the observation of Bohr's strong formulation of complementarity.
We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability tradeoff via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM superconducting transmon processor. A detailed analysis of the results is provided. Despite finding good agreement with theory at a coarse level, we also identify small but persistent systematic deviations preventing the observation of full particlelike and wavelike statistics. We understand them by carefully modeling two-qubit gates, showing that even small coherent errors in their implementation preclude the observation of Bohr's strong formulation of complementarity.
Bohr’s principle of complementarity, after gaining contributions from several researchers, moved from a qualitative analysis to a quantitative analysis through what we call today complementarity relations (CR). This change made it possible to quantify aspects of path superposition and distinguishability (predictability and entanglement) in a single experimental apparatus, for example, the Mach-Zehnder interferometer (MZI), gaining historical appeal in the quantification of path superposition through interferometric visibility. Furthermore, CR of quantum coherence, predictability and entanglement functions that are dependent on the quantum state, have also gained relevance in this area of research. In this dissertation, based on other research, we were directed to carry out two works involving the IMZ and analysis through CR. In the first work, we build a version of the MZI and show that interferometric visibility is not always able to correctly quantify the path superposition within the MZI for two-path systems. We found that CR involving quantum coherence end up reflecting the expected behavior for the photon in this same experimental apparatus. In the second work, we performed an integral analysis, through the complete CR, of the entangled quantum eraser (EQE). In this experimental apparatus, we consider a variable partially-polarizing beam splitter (VPPBS) that can produce path superposition of the horizontal and vertical polarizations entering the MZI. Due to the inclusion of the VPPBS, part of the experimental apparatus of the standard quantum eraser was modified, so that we need to perform Bell’s basis measurements of the degree of freedom of the polarizations of the two entangled photons. Therefore, the analysis of the EQE, through the CR, ends up being much richer, producing situations where there are even partial erasures of the information available before the erasure process. In both papers, we verified our theoretical findings by implementing experiments on IBM’s quantum computers.
Wave--particle duality demonstrates the peculiar nature of quantum mechanics. In which-way experiments, depending on the measurement scheme, a particle exhibits either wave-like or particle-like properties, as summarized by Bohr's principle of complementarity. In this work, we implement Mach-Zehnder (MZ) interferometry on a two-dimensional (2D) superconducting quantum processor. With precise control of the which-way measurement strength, we demonstrate the transition of a photon from wave-like to particle-like behavior. Furthermore, by performing quantum state tomography on two qubits located in the two paths, we demonstrate that which-way measurements break the entanglement and coherence between the two paths and cause information leakage from the quantum system to the environment. To capture this behavior quantitatively, we derive complementarity relations between the entropy and the fringe visibility. By applying a continuous which-way measurement during the evolution, we also observe the quantum Zeno effect that partially obstructs the interferometer path, giving rise to nonmonotonic behavior of purity and von Neumann entropy. Our experiments provide a detailed characterization of the full interferometer dynamics, reveal the relation between wave--particle duality and quantum information, and demonstrate the potential of superconducting quantum processors for testing quantum foundations under high precision and controllability.
Abstract Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementary principle, but the quantitative relation between this entanglement and the fringe visibility remains untouched upon for an initial mixed state. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled with a which-path detector to a certain degree. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The results demonstrate quantum entanglement is the mechanism for prohibiting any detector from acquiring which-path information without deteriorating the interference pattern, which was not confirmed previously.
The principle of complementarity is one of the cornerstones of quantum theory. The aim of this study was to advance our understanding of complementarity by analyzing the role of delayed choice and quantum erasers in two-slit experiments, and by proposing experiments for verifying the analysis. The analysis is based on models consisting of measurable spaces and probability measures involved in the experiments. The main findings are as follows: (a) The complementarity principle manifests itself in such a way that wave and particle behaviors cannot be simultaneously observed almost surely with respect to any single, fixed measure. (b) Described by different measures, complementary properties can coexist in the same experimental setup. (c) Which-way information will not preclude or erase interference fringes. (d) Delayed choice and quantum erasers are irrelevant to testing complementarity. (e) It is possible for us to know through which slit each quantum object passed almost surely with respect to the measure corresponding to the slit while the interference pattern is intact. Based on the experiments analyzed, realizable experiments are proposed for verifying the above results.
Wave-particle complementarity lies at the heart of quantum mechanics. To illustrate this mysterious feature, Wheeler proposed the delayed-choice experiment, where a quantum system manifests the wave- or particle-like attribute, depending on the experimental arrangement, which is made after the system has entered the interferometer. In recent quantum delayed-choice experiments, these two complementary behaviors were simultaneously observed with a quantum interferometer in a superposition of being closed and open. We suggest and implement a conceptually different quantum delayed-choice experiment by introducing a which-path detector (WPD) that can simultaneously record and neglect the system's path information, but where the interferometer itself is classical. Our experiment is realized with a superconducting circuit, where a cavity acts as the WPD for an interfering qubit. Using this setup, we implement the first twofold delayed-choice experiment, which demonstrates that the system's behavior depends not only on the measuring device's configuration that can be chosen even after the system has been detected but also on whether we a posteriori erase or mark the which-path information, the latter of which cannot be revealed by previous quantum delayed-choice experiments. Our results represent the first demonstration of both counterintuitive features with the same experimental setup, significantly extending the concept of quantum delayed-choice experiment.
We present various experiments demonstrating the mutual exclusivity of observing interference and which-path information, as demanded by Bohr's complementarity principle. Using photon pairs created in parametric down-conversion, no which-path measurements need to be performed on the interfering photon itself. Instead the other photon can be used to introduce distinguishability, which consequently destroys interference. However, a suitable measurement erases this distinguishability and interference can be recovered.