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arXiv:1210.6463 · Optics Express

Direct characterization of linear-optical networks

Saleh Rahimi-Keshari, Matthew A. Broome, Robert Fickler, Alessandro Fedrizzi, Timothy C. Ralph, Andrew G. White

Published May 28, 2013• 106 citations
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Abstract

We introduce an efficient method for fully characterizing multimode linear-optical networks. Our approach requires only a standard laser source and intensity measurements to directly and uniquely determine all moduli and non-trivial phases of the matrix describing a network. We experimentally demonstrate the characterization of a 6×6 fiber-optic network and independently verify the results via nonclassical two-photon interference.

DOI
10.1364/oe.21.013450

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We introduce an efficient method for fully characterizing multimode linear-optical networks. Our approach requires only a standard laser source and intensity measurements to directly and uniquely determine all moduli and non-trivial phases of the matrix describing a network. We experimentally demonstrate the characterization of a 6×6 fiber-optic network and independently verify the results via nonclassical two-photon interference.
The paper introduced an efficient and simple method for characterizing any multi-mode linear photonic network, by directly measuring all moduli and phases of the matrix that relates creation operators of the input and output modes. The method employs a readily available standard laser source and photodetectors, and eliminates the need for nonclassical interference and single-photon detectors. It requires 2N-1 configurations for measuring all nontrivial parameters of the matrix describing N-mode linear photonic network. The authors used this method to experimentally characterize an integrated device, a 6×6 fused-fibre coupler, and highlight its precision by comparing measured quantum interference patterns with those predicted using the classically-estimated matrix. The obtained interference patterns are in excellent agreement with those predicted by the measured matrix using our method.
Linear photonic devices comprised of simple beamsplitters and phase shifters can implement any unitary operator for quantum information processing. The significant practical challenge is to characterize such an interferometric device once it is built. Performing quantum process tomography requires the full suite of quantum tools such as N-mode quantum state preparation and measurement, and is, despite progress on more efficient methods, slow and impractical for large interferometric devices. Here we introduce a simple technique to characterize the unitary matrix of a linear photonic device using standard laser sources and photodetectors, without the requirement for active locking or single-photon sources. Our method is precise and efficient, requiring only 2N-1 measurement configurations for a N-path network. We use it experimentally to characterise an integrated 3x3 fused-fibre coupler and highlight its precision by comparing measured quantum interference patterns with those predicted using the classically-estimated unitary. We observe excellent agreement between the two experimental methods.
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.
We combine single- and two-photon interference procedures for characterizing any multi-port linear optical interferometer accurately and precisely. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to curve simulated using measured source spectra. We employ bootstrapping statistics to quantify the resultant degree of precision. A scattershot approach is devised to effect a reduction in the experimental time required to characterize the interferometer. The efficacy of our characterization procedure is verified by numerical simulations.
Linear-optic photonic networks with multiple single-photon inputs are attracting attention due to their great potential for quantum computation, quantum communication, and quantum sensing. They are also essential for verifying quantum advantages via boson sampling schemes. The quantum coherence of generated multimode–multiphoton states is crucial for various applications. However, the coherence is invisible in the normally obtained photon number distributions, which strictly limits the efficiency of entanglement verification between multimode–multiphoton systems since the required resources for quantum state tomography increase exponentially as the number of photons/modes increases. In this paper, we report the experimental demonstration of direct and efficient verification of entanglement between two multimode–multiphoton systems (one photon in three modes and two photons in three modes) using just two sets of classical correlation tables with and without a discrete Fourier transformation of the optical modes, clearly demonstrating a dramatic reduction in the resources required for entanglement verification. Our experimental demonstration paves the way to understanding the coherence and entanglement of multi-partite systems, not only for photons but for other quantum resources with high-dimensional degrees of freedom.
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their effective utilization and scalability. In this work, we present the method for reconstructing the transfer matrix of a linear optical interferometer based on the analysis of cross-correlation functions of photon counts between pairs of output modes. Our approach accounts for losses and photon indistinguishability, making it robust to experimental imperfections. By minimizing the requirements for the input states, the method simplifies the experimental implementation. We demonstrate the effectiveness of our technique through theoretical modeling and experimental validation in a 4-mode programmable integrated optical interferometer. The results show high fidelity in matrix reconstruction and successful application in boson sampling experiments. In addition, we provide a comprehensive formalism for correlation functions and discuss the robustness of the method to measurement errors. This work offers a practical and efficient solution for characterizing linear-optical networks, paving the way for scaling up photonic quantum technologies.