Abstract Holographic metasurfaces and their applications have garnered significant attention owing to their role in polarization control. In this study, we demonstrate that the quantum properties of holographic metasurfaces can be obtained by quantum state tomography (QST) and quantum process tomography (QPT). We perform QST to obtain the experimental output states by extracting information from holograms encoded on the holographic metasurface, and develop a QPT-based method to estimate the quantum process of the metasurface. The theoretical output states derived from the estimated quantum process are in good agreement with the experimental output states, proving the effectiveness of our method. Our work not only provides theoretical and experimental analysis for understanding the quantum properties of holographic metasurfaces, but also paves the way for the application of holographic metasurfaces in quantum field.
Abstract Holographic metasurfaces and their applications have garnered significant attention owing to their role in polarization control. In this study, we demonstrate that the quantum properties of holographic metasurfaces can be obtained by quantum state tomography (QST) and quantum process tomography (QPT). We perform QST to obtain the experimental output states by extracting information from holograms encoded on the holographic metasurface, and develop a QPT-based method to estimate the quantum process of the metasurface. The theoretical output states derived from the estimated quantum process are in good agreement with the experimental output states, proving the effectiveness of our method. Our work not only provides theoretical and experimental analysis for understanding the quantum properties of holographic metasurfaces, but also paves the way for the application of holographic metasurfaces in quantum field.
Metasurfaces, with their capability to control all possible dimensions of light, have become integral to quantum optical applications, including quantum state generation, operation, and tomography. We utilize a metasurface to generate polarization–hologram hybrid entanglement between a signal–idler photon pair to construct a quantum hologram. The properties of the quantum hologram can be revealed by collapsing the polarization degree of freedom of the idler photon, inducing interference between two holographic states of the signal photon as a meaningful and selective erasure of the holographic content. On the contrary, interference disappears when the idler photon is detected without observing polarization. This process can be further interpreted as a quantum holographic eraser, where the erasing action is visualized with erased contents in holograms. Our construction of a polarization–hologram hybrid entangled state with metasurfaces will be useful for quantum communication with enhanced robustness, anticounterfeiting applications through the additional quantum degrees of freedom or phase difference between two holographic states, and as an emerging platform for exploring fundamental quantum concepts for entanglement and nonlocality.
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of quantum gates, that may be used as the building blocks of quantum computers. We here consider unitary (possibly dense, i.e. without sparsity constraints) processes, which corresponds to isolated systems. Moreover, we develop a QPT method applicable to a significant number of qubits and hence to a high state space dimension, which allows one to tackle more complex problems. Using the unitarity of the process allows us to propose a method that first achieves part of QPT by performing an eigenanalysis of the estimated density matrix of a process output. We then complete the QPT by using another state differently. The relevance of our method is validated by means of simulations.
Engineering of quantum computers requires reliable characterization of qubits, quantum operations, and even the entire hardware. Quantum tomography is an indispensable framework in quantum characterization, verification, and validation (QCVV), which has been widely accepted by researchers. According to the tomographic target, quantum tomography can be categorized into quantum state tomography (QST), quantum process tomography (QPT), gate set tomography (GST), process tensor tomography (PTT), and instrument set tomography (IST). Standard quantum tomography toolkits generally consist of basic linear inverse methods and statistical maximum likelihood estimation (MLE) based methods. Furthermore, the performance of standard methods, including effectiveness and efficiency, has been further developed by exploiting Bayesian estimation, neural networks, matrix completion techniques, etc. In this review, we introduce the fundamental quantum tomography techniques, including QST, QPT, GST, PTT, and IST. We first introduce the details of basic linear inverse methods. Then, the framework of MLE methods with constraints is summarized. Finally, we briefly introduce recent further research in developing the performance of tomography. This review provides a primary getting-start in developing quantum tomography, which promotes quantum computer development.
Metasurfaces present novel prospects for compacted quantum technologies by providing precise manipulation of amplitude, phase, and polarization of the incident light. Utilizing the advanced polarization control and multiplexing capabilities of metasurfaces, the capacity for detecting and processing quantum information can be enhanced. In this work, we optimize metasurface fabrication using electron-beam lithography and develop a custom SEM image recognition program for precise structure assessment and improved imaging quality. We achieve holographic imaging under quantum state incidence, enabling the reconstruction of quantum state information from the resulting meta-holography.
Quantum state tomography (QST) refers to any method that allows one to reconstruct the accurate representation of a quantum system based on data obtainable from an experiment. In this paper, we concentrate on theoretical methods of quantum tomography, but some significant experimental results are also presented. Due to a considerable body of literature and intensive ongoing research activity in the field of QST, this overview is restricted to presenting selected ideas, methods, and results. First, we discuss tomography of pure states by distinguishing two aspects—complex vector reconstruction and wavefunction measurement. Then, we move on to the Wigner function reconstruction. Finally, the core section of the article is devoted to the stroboscopic tomography, which provides the optimal criteria for state recovery by including the dynamics in the scheme. Throughout the paper, we pay particular attention to photonic tomography, since multiple protocols in quantum optics require well-defined states of light.