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arXiv:2203.06368

Complex structure and characterization of multi-photon split states in integrated circuits

Jihua Zhang, Andrey A. Sukhorukov

Published Mar 12, 2022• 0 citations
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Abstract

Multi-photon split states, where each photon is in a different spatial mode, represent an essential resource for various quantum applications, yet their efficient characterization remains an open problem. Here, we formulate the general structure of their reduced spatial density matrices and identify the number of real and complex-valued independent coefficients, which in particular completely determine the distinguishability of all photons. Then, we show that this density matrix can be fully characterized by measuring correlations after photon interference in a static integrated circuit, where the required outputs scale sub-quadratically versus the number of photons. We present optimized circuit designs composed of segmented coupled waveguides, representing a linear optical neural network, which minimize the reconstruction error and facilitate robustness to fabrication deviations.

DOI
10.48550/arxiv.2203.06368

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Multi-photon split states, where each photon is in a different spatial mode, represent an essential resource for various quantum applications, yet their efficient characterization remains an open problem. Here, we formulate the general structure of their reduced spatial density matrices and identify the number of real and complex-valued independent coefficients, which in particular completely determine the distinguishability of all photons. Then, we show that this density matrix can be fully characterized by measuring correlations after photon interference in a static integrated circuit, where the required outputs scale sub-quadratically versus the number of photons. We present optimized circuit designs composed of segmented coupled waveguides, representing a linear optical neural network, which minimize the reconstruction error and facilitate robustness to fabrication deviations.
Multiphoton split states, where each photon is in a different spatial mode, represent an essential resource for various quantum applications, yet their efficient characterization remains an open problem. Here, we formulate the general structure of their reduced spatial density matrices and identify the number of real and complex-valued independent coefficients, which in particular completely determine the distinguishability of all photons. Then, we show that this density matrix can be fully characterized by measuring correlations after photon interference in a static integrated circuit, where the required number of outputs scales subquadratically versus the number of photons. We present optimized circuit designs composed of segmented coupled waveguides, representing a linear optical neural network, which minimize the reconstruction error and facilitate robustness to fabrication deviations.
Multi-photon split states, where each photon is in a different input mode, represent an essential resource for various quantum applications. Accordingly, characterisation of such states is important from the fundamental and practical perspectives. We propose a segmented coupled waveguide array as a new form of compact low-loss quantum circuit and apply it for the scalable multi-photon split state tomography with optimized performance and no need of reconfigurability. We develop an optimization algorithm to design the array with minimally necessary number of waveguides and smallest sensitivity to noise in the tomography. Such a novel platform can enable fast, scalable, and fully integrated quantum systems.
Summary form only given. Full characterization of quantum states is increasingly important as ever more complex quantum systems are realized. Quantum state tomography of these systems is a difficult task because individual measurements only give partial information about the underlying density matrix of the system. Thus, conventionally the measurement apparatus must be reconfigured to take multiple measurements in order to fully determine the density matrix. It is accepted that for an W-qubit system an exponentially increasing number of measurements are needed [1]. As a consequence, the complexity of typical quantum state tomography grows exponentially with increasing photon number, which makes characterizing large quantum systems highly challenging. We formulate a concept of on-chip quantum tomography where the complexity scales linearly with the number of photons. This is achieved by using a single specially designed non-reconfigurable linear optical circuit as in Fig. 1(a). Crucially, the number of waveguides in this circuit scales linearly with the number of photons in the state to be measured. Furthermore, our approach is simple and robust, and we demonstrate it experimentally with a specially designed photonic chip.
With recent advances in nanophotonics, metasurfaces based on nano-resonators have facilitated novel types of optical devices. In particular, the interplay between different degrees of freedom, involving polarization and spatial modes, boosted classical polarization measurements and imaging applications. However, the use of metasurfaces for measuring the quantum states of light remains largely unexplored. Conventionally, the task of quantum state tomography is realized with several bulk optical elements, which need to be reconfigured multiple times. Such setups can suffer from decoherence, and there is a fundamental and practical interest in developing integrated solutions for measurement of multi-photon quantum states. We present a new concept and the first experimental realization of all-dielectric metasurfaces with no tuneable elements for imaging-based reconstruction of the full quantum state of entangled photons. Most prominently, we implement multi-photon interferometric measurements on a sub-wavelength thin optical element, which delivers ultimate miniaturization and extremely high robustness. Specifically, we realize a highly transparent all-dielectric metasurface, which spatially splits different components of quantum-polarization states. Then, a simple one-shot measurement of correlations with polarization-insensitive on-off click detectors enables complete reconstruction of multi-photon density matrices with high precision. In our experiment, we prepare sets of polarization states and reconstruct their density matrices with a high fidelity of over 99% for single photon states and above 95% for two-photon states. Our work provides a fundamental advance in the imaging of quantum states, where multi-photon quantum interference takes place at sub-wavelength scale.
Multimode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication and sensing, to computation, including optical neural networks, optical reservoir computing, or simulation of complex physical systems. The realization of such routines requires high levels of control and tunability of the parameters that define the operations carried out by the device. This requirement becomes particularly crucial in light of recent technological improvements in integrated photonic technologies, which enable the implementation of progressively larger circuits embedding a considerable amount of tunable parameters. We formulate efficient procedures for the characterization of optical circuits in the presence of imperfections that typically occur in physical experiments, such as unbalanced losses and phase instabilities in the input and output collection stages. The algorithm aims at reconstructing the transfer matrix that represents the optical interferometer without making any strong assumptions about its internal structure and encoding. We show the viability of this approach in an experimentally relevant scenario, defined by a tunable integrated photonic circuit, and we demonstrate the effectiveness and robustness of our method. Our findings can find application in a wide range of optical setups, based on both bulk and integrated configurations.
Integrated single-photon detectors open new possibilities for monitoring inside quantum photonic circuits. We present a concept for the in-line measurement of spatially-encoded multi-photon quantum states, while keeping the transmitted ones undisturbed. We theoretically establish that by recording photon correlations from optimally positioned detectors on top of coupled waveguides with detuned propagation constants, one can perform robust reconstruction of the density matrix describing the amplitude, phase, coherence and quantum entanglement. We report proof-of-principle experiments using classical light, which emulates single-photon regime. Our method opens a pathway towards practical and fast in-line quantum measurements for diverse applications in quantum photonics.