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.
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.
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a duality relation between the quantum coherence and the path distinguishability. For two-path interference, the quantum coherence is identical to the interference fringe visibility, and the relation reduces to the well-known complementarity relation. The duality relation continues to hold in the case where mixedness is introduced due to possible decoherence effects.
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 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.
This thesis is a dissemination of the work I have done in the last four years, under supervision of Prof. Tabish Qureshi. The central theme is towards the understanding of entanglement as a physical resource and looking for its possible applications. This thesis contains six chapters.The Chapter 1 provides the background knowledge for the thesis work, which includes the mathematical formalism of quantum mechanics and the conceptual understanding of entanglement.The Chapter 2 unfolds the idea of fundamental concepts such as Bohr’s complementarity principle, quantum interference, which-path information, their trade-off relation, quantum eraser and also discuss how these issues play their role in building the foundations of quantum theory.The Chapter 3 is devoted to three slit interference experiments. The interference experiment is one of the most prominent concept of quantum theory. The two slit interference set-up is broadly studied and clearly understood, the synopsis for more than two slits are still not clear, recently a focussed research has been shifted towards three slit set-ups. We study the trade-off relation for three slit experiment in terms of visibility and the path distinguishability based on unambiguous quantum state discrimination (UQSD) method.The Chapter 4 discusses the wave-particle duality for multi-slit interference. Several attempts have been made in the past two decades to procure the trade-off relation for multi-slit experiments, yet a satisfactory answer was lacking. We obtain an analogous wave particle duality relation in terms of coherence and path-distinguishability based on UQSD. The role of coherence in building the interference pattern is largely admitted and their amount is readily stated by fringe visibility. Recently coherence has been understood as an information theoretical resource. We explore the measure of coherence as a wave quantifier rather than well known fringe visibility. We also analyze a recently proposed multi-path relation of Bagan et al. which claims to be in Englert’s form. We show that the proposed relation does not hold the essence of complementarity. We also derive a relation similar to Englert’s one to fill the exigency and to explicate its equivalence with our earlier proposed relation.The Chapter 5 discuss the scenario when the source is considered to be entangled. The entangled photon exhibits an interesting phenomenon known as ghost interference. The trade-off relation for two and three slit ghost experiment has been formulated, and also a doable quantum eraser has been proposed.The Chapter 6 aims to use the entanglement as a resource and develop the quantum information technologies, with Quantum Key Distribution (QKD). We propose a QKD protocol using entangled qubits which is shown to add an additional security over the well known BB84 protocol.
It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. An alternative interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability, and the I concurrence (quantifying the entanglement between the quanton and the path detector) are shown to follow a tight triality relation. It quantifies the essential role that entanglement plays in multipath quantum complementarity.
Interference results when a quantum particle is free to choose among a few indistinguishable paths. A canonical example of Bohr's complementarity principle [1] is a two-path interferometer with an external detector coupled to one of the paths. Then, interference between the two paths vanishes (i.e. dephasing) if one is able to detect, even in principle, the path taken by the particle. This type of which path (WP) experiment was already executed with photons, cooled atoms, neutrons, solitons, and more recently with electrons in a mesoscopic system [2]. In the latter experiment path determination was provided by inducing a change in the current flowing through the detector. In the present experiment we perform a more intriguing WP determination: only a phase change is being induced in the detector while the current remains unaffected. We show that such detector-interferometer interaction can be understood both, from the WP information obtained by the detector, or alternatively by understanding the disturbance in the interferometer caused by the detector. Moreover, we address the subtle role of detector coherency and point out difficulties in the intuitive interpretation of the experiment.