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arXiv:1910.08779 · Physical Review Letters

Experimental Quantification of Coherence of a Tunable Quantum Detector

Huichao Xu, Feixiang Xu, Thomas Theurer, Dario Egloff, Zi-Wen Liu, Nengkun Yu, Martin Bodo Plenio, Lijian Zhang

Published Aug 5, 2020• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.125.060404

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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
Abstract In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of positive-operator-valued measure components. This quantification provides a lower bound on the robustness of measurement-coherence that has an operational meaning as the maximal advantage over all incoherent measurements in state discrimination tasks. Finally, we propose an experimental scheme to assess our quantification of measurement-coherence and demonstrate it by performing an experiment using a single qubit on IBM Q processor.
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.
Characterization of quantum states and detectors is a key task in rapidly emerging optical quantum science and technology. First, we introduce and experimentally demonstrate a noise-robust quantum state characterization protocol using photon-number-resolving (PNR) measurements. Unlike conventional continuous variable state tomography methods, our method utilizes computationally efficient semi-definite programming (SDP) and can be used to accurately reconstruct the state even after loss a known loss. The protocol is demonstrated for a weak coherent state as well as a single-photon Fock state. Next, we propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector’s Positive-Operator-Value-Measure (POVM) elements via weak-field homodyne technique. We also report our experimental progress on characterizing a superconducting transition-edge sensor for PNR measurements.
Quantum optics is central to emerging quantum technologies such as quantum metrology and quantum information. The continuous variable (CV) approach to encoding information in a physical system, for example the electromagnetic field quadratures has significant advantages over discrete variables (DV) encoding. CV offers higher density encoding in a single optical state and on-demand state preparation for example. However, techniques for CV preparation, manipulation and measurement are not as well developed as the corresponding DV approach. In this thesis we present methods to characterize quantum detectors that operate in the CV regime, and discuss their application to CV state preparation. A quantum detector is described by its positive operator valued measure (POVM) set, with one operator for each measurement outcome. We present an experimental scheme for detector tomography, that is reconstruction of the POVM set of an unknown detector by means of measurement outcomes for a set of tomographically complete input states. We use this scheme to experimentally determine the POVM set of an avalanche photodiode (APD) and a time-multiplexed-detector (TMD) and compare the results to models of the detectors. We introduce a weak-homodyne photon-number-resolving detector (PNRD) , which uses a weak local oscillator beam to set a phase reference for the detection process. We develop a theoretical description of the sensitivity regimes for this detector using the Wigner phase space picture. We also present experimental detector tomography for a weak-homodyne detector based on two APDs. In many cases it is sufficient to calibrate the efficiencies of previously characterized PNRDs. We experimentally demonstrate a scheme using correlated photons produced by spontaneous parametric downconversion (SPDC) to determine the efficiencies of PNRDs, based on the photon number statistics of the source. The same SPDC source is also used to demonstrate preparation of photonic states in the photon number basis and for a first proof-of-principle experiment with a weak-homodyne PNRD based on a TMD.
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.