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arXiv:1505.03297 · New Journal of Physics

Experimental quantum tomography of a homodyne detector

Samuele Grandi, Alessandro Zavatta, Marco Bellini, Matteo G. A. Paris

Published Apr 25, 2017• 43 citations
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Abstract

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.

DOI
10.1088/1367-2630/aa6f2c

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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.
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.
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of different observables, obtained on identical copies of the same system. Alternatively, it consists in maximizing an appropriate likelihood function defined on the same data. The procedure can be also used to completely characterize an unknown apparatus. Here we focus on the electromagnetic field, where the tomographic observables are obtained from homodyne detection.