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Physical Review A

Efficient tomography of coherent optical detectors

Xinyu Chen, Feixiang Xu, Huichao Xu, Lijian Zhang

Published Nov 30, 2022• 1 citation
Publisher

Abstract

We propose an efficient tomography method to address the reconstruction complexity of any general quantum coherent-optical detectors. By extracting the linear loss from the entire detection system, we obtain the effective positive-operator-valued measure in matrix representations with a much smaller size. We apply this method to reconstruct a typical coherent detector: the weak-field homodyne detector. The method also highlights the effects of linear loss on nonclassical features of coherent optical detectors.Received 14 August 2022Accepted 16 November 2022DOI:https://doi.org/10.1103/PhysRevA.106.L051702©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum tomographyQuantum Information

DOI
10.1103/physreva.106.l051702

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We propose an efficient tomography method to address the reconstruction complexity of any general quantum coherent-optical detectors. By extracting the linear loss from the entire detection system, we obtain the effective positive-operator-valued measure in matrix representations with a much smaller size. We apply this method to reconstruct a typical coherent detector: the weak-field homodyne detector. The method also highlights the effects of linear loss on nonclassical features of coherent optical detectors.Received 14 August 2022Accepted 16 November 2022DOI:https://doi.org/10.1103/PhysRevA.106.L051702©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum tomographyQuantum Information
We suggest and demonstrate a tomographic method to characterise homodyne detectors at the quantum level.The positive operator measure associated with the detector is expanded in a quadrature basis and probed with a set of coherent states.The coefficients of the expansion are then retrieved using a least squares algorithm.Our model is general enough to describe different implementations of the homodyne setup, and it has proven capable of effectively describing the detector response to different tomographic sets.We validate the reconstructed operator measure on nonclassical states and exploit results to estimate the overall quantum efficiency of the detector.
Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect coherence from the measurement statistics. Based on a recently developed resource theory of quantum operations, here we quantify experimentally the ability of a typical quantum-optical detector, the weak-field homodyne detector, to detect coherence. We derive an improved algorithm for quantum detector tomography and apply it to reconstruct the positive-operator-valued measures of the detector in different configurations. The reconstructed positive-operator-valued measures are then employed to evaluate how well the detector can detect coherence using two computable measures. As the first experimental investigation of quantum measurements from a resource theoretical perspective, our work sheds new light on the rigorous evaluation of the performance of a quantum measurement apparatus.
We propose a general method for reconstructing directly the density matrix of a single light mode in optical homodyne tomography. In our scheme the density matrix 〈a\ensuremath{\Vert}\ensuremath{\rho}^\ensuremath{\Vert}${\mathit{a}}^{\ensuremath{'}}$〉 is obtained by averaging a set of pattern functions ${\mathit{F}}_{\mathit{aa}}^{\ensuremath{'}}$(${\mathit{x}}_{\mathrm{\ensuremath{\theta}}}$,\ensuremath{\theta}) with respect to the homodyne data ${\mathit{x}}_{\mathrm{\ensuremath{\theta}}}$. The functions show the typical features of the quadrature distributions for the corresponding density-matrix elements. It is also possible to compensate the effect of detection losses which requires, however, extra effort in both experimental and numerical precision. We calculate the pattern functions for the coherent-state and Fock representations and study their properties. We believe that our method is the most efficient way for reconstructing the density matrix from homodyne measurements.
Abstract Conventional tomographic techniques are becoming increasingly infeasible for reconstructing the operators of quantum devices of growing sophistication. We describe a novel tomographic procedure using coherent states, which begins by reconstructing the diagonals of the operator and then each successive off-diagonal in a recursive manner. Each recursion is considerably more efficient than reconstructing the operator in its entirety, and each successive recursion involves fewer parameters. We apply our technique to reconstruct the positive-operator-valued measure corresponding to a recently developed coherent optical detector with phase sensitivity and number resolution. We discuss the effect of various parameters on the reconstruction accuracy. The results show the efficiency of the method and its robustness to experimental noise.