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Inline multiphoton quantum state tomography

Kai Wang, Sergey V. Suchkov, James Titchener, Alexander Szameit, Andrey A. Sukhorukov

Published Dec 30, 2019• 0 citations
Publisher

Abstract

Latest advances in integrated single-photon detectors offer possibilities for gaining information inside quantum photonic circuits. We introduce a concept and provide experimental evidence for the inline tomographic mea- surement of multiphoton quantum states, while keeping the transmitted ones undisturbed. We establish that by recording photon correlations from optimally positioned detectors on top of coupled waveguides with de- tuned propagation constants, one can perform robust reconstruction of multiphoton density matrices describing the amplitude, phase, coherence and quantum entanglement. We report proof-of-principle experiments. Our method opens a pathway towards practical and fast inline state tomography for diverse applications in quantum photonics.

DOI
10.1117/12.2539146

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Latest advances in integrated single-photon detectors offer possibilities for gaining information inside quantum photonic circuits. We introduce a concept and provide experimental evidence for the inline tomographic mea- surement of multiphoton quantum states, while keeping the transmitted ones undisturbed. We establish that by recording photon correlations from optimally positioned detectors on top of coupled waveguides with de- tuned propagation constants, one can perform robust reconstruction of multiphoton density matrices describing the amplitude, phase, coherence and quantum entanglement. We report proof-of-principle experiments. Our method opens a pathway towards practical and fast inline state tomography for diverse applications in quantum photonics.
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.
The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density matrices require the detection of both photons unless a priori information is available. Based on the concept of quantum-induced coherence by path identity, we present an approach to quantum state tomography that circumvents the requirement of detecting both photons. We show that an arbitrary two-qubit density matrix, which can contain up to fifteen free parameters, can be fully reconstructed from single-photon measurement data without any postselection and a priori information. In addition to advancing an alternative approach to quantum state measurement problems, our results also have notable practical implications. A practical challenge in quantum state measurement arises from the fact that effective single-photon detectors are not readily accessible for a wide spectral range. Our method, which eliminates the need for coincidence measurements, enables quantum state tomography in the case where one of the two photons is challenging or impossible to detect. It therefore opens the door to measuring quantum states hitherto inaccessible.
We have performed quantum-state tomography on several different single-photon entangled states, that is, states in which a single photon is shared between two possible paths. We begin by doing a tomographic reconstruction of density matrices in the subspace where a single photon is shared by two spatial modes. In this subspace we are able to create high-fidelity, path-entangled states. Also within this subspace we use the Akaike information criterion and Monte Carlo simulations to help us estimate the amount and source of state drift in our system. We find that the primary state drift is due to phase drifts and fluctuations on the order of $\ensuremath{\pi}/400$ in our experimental apparatus. We then use the single-photon subspace density matrices and further measurements to estimate density matrices in the larger space consisting of two modes containing up to one photon each. In this larger space we find that the concurrence of the density matrices is $C\ensuremath{\cong}0.08$ and is greater than 0 by at least 45 standard deviations, indicating that our states are indeed entangled.
Quantum state tomography (QST) is a fundamental technique for characterizing quantum states, crucial for validating quantum technologies. However, traditional QST methods often suffer from limitations in measurement efficiency and accuracy, particularly when dealing with complex quantum systems. This work presents an advanced approach to QST utilizing entangled photon sources and a meticulously designed measurement strategy. The core of this method lies in exploiting the correlations inherent in entangled photon pairs to significantly enhance the reconstruction process. We detail a novel scheme that minimizes measurement errors and maximizes the information extracted from each measurement, leading to a substantial improvement in both the accuracy and resolution of the reconstructed quantum state. The theoretical framework outlines the key equations and algorithms used for state reconstruction, focusing on a practical implementation. The results presented suggest a pathway towards more robust and reliable QST, paving the way for more accurate characterization of quantum systems and the development of advanced quantum applications.
This work proposes to carry out a study on integrated photonic circuits. Our goal is to develop a methodology for obtaining the parameters of a photonic circuit that allows us to perform a set of quantum operations necessary for the realization of a given task or quantum processing. More specifically, the quantum tasks involve the implementation of a POVM (Positive Operator Value Measure) through integrated photonic circuits. Thus, we seek to obtain optimized configurations for these devices so that the reduction of their structural complexity simplifies their manufacturing process. In addition, it is also our goal that such objects are robust against errors and losses and that the experimental applications that involve them present a minimization of the time necessary for their realization. We studied the symmetries of the proposed POVMs to, from them, configure the circuit in an optimized way. Initially, we studied the case of quantum state tomography for qubits and qutrits. We obtained planar circuits that had a smaller number of optical elements and an optical depth than those obtained by methods already known in the literature. In addition, these circuits implement all POVM elements at once, making it possible to obtain all their associated probabilities at once, minimizing the time spent on the experiment compared to experiments on an optical table or with reconfigurable circuits, where it is necessary to make changes to the configuration of the experimental apparatus from one POVM element to another. Looking for a way to generalize our protocol to larger systems, we developed a method to obtain three-dimensional photonic circuits that can be used in the experimental realization of quantum state tomography in qudits of any finite dimension. Our protocol generates circuits whose number of beam splitters and optical depth scale with functions less than in other protocols already known, showing a drastic reduction in their complexity. In addition, these circuits were highly robust in relation to the occurrence of losses. The same protocol used to obtain three-dimensional circuits for performing quantum tomography can be used to obtain circuits to implement quantum coherence measurements. The circuits obtained here also have the same advantages as the tomographic case.
In this work we develop an experimental procedure to interrogate the single- and multiphoton scattering matrices of an unknown quantum system interacting with propagating photons. Our proposal requires coherent state laser or microwave inputs and homodyne detection at the scatterer's output, and provides simultaneous information about multiple-elastic and inelastic-segments of the scattering matrix. The method is resilient to detector noise and its errors can be made arbitrarily small by combining experiments at various laser powers. Finally, we show that the tomography of scattering has to be performed using pulsed lasers to efficiently gather information about the nonlinear processes in the scatterer.