Ability of entanglement and purity to help to detect systematic experimental errors
Julia Freund, Francesco Basso Basset, Tobias M. Krieger, Alessandro Laneve, Mattia Beccaceci, Michele B. Rota, Quirin Buchinger, Saimon F. Covre da Silva, Sandra Stroj, Sven Höfling, Tobias Huber, Richard Kueng, Armando Rastelli, Rinaldo Trotta, Otfried Gühne
Measurements are central in all quantitative sciences, and a fundamental challenge is to make observations without systematic measurement errors. This holds in particular for quantum information processing, where other error sources, such as noise and decoherence, are unavoidable. Consequently, methods for detecting systematic errors have been developed, but the required quantum state properties are yet unexplored. We theoretically develop a direct and efficient method to detect systematic errors in quantum experiments and demonstrate it experimentally using quantum state tomography of photon pairs emitted from a semiconductor quantum dot. Our method can be scaled to multiqubit systems, and we find that entanglement and quantum states with high purity can help identify systematic errors.
Measurements are central in all quantitative sciences, and a fundamental challenge is to make observations without systematic measurement errors. This holds in particular for quantum information processing, where other error sources, such as noise and decoherence, are unavoidable. Consequently, methods for detecting systematic errors have been developed, but the required quantum state properties are yet unexplored. We theoretically develop a direct and efficient method to detect systematic errors in quantum experiments and demonstrate it experimentally using quantum state tomography of photon pairs emitted from a semiconductor quantum dot. Our method can be scaled to multiqubit systems, and we find that entanglement and quantum states with high purity can help identify systematic errors.
Abstract Entanglement and coherence are fundamental properties of quantum systems, promising to power near-future quantum technologies, such as quantum computation, quantum communication, and quantum metrology. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing.
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction of the system state. We show that one can extract quantitative bounds to the relative entropy of coherence and the coherent information, coherence and entanglement quantifiers respectively, by a limited number of purity measurements. The scheme is readily implementable with current technology to verify quantum computations in large scale registers, without carrying out expensive state tomography.
A prime goal of quantum tomography is to provide quantitatively rigorous characterization of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in quantum information science. A range of techniques exist to enable the calculation of errors, such as Monte-Carlo simulations, but their quantitative value is arguably fundamentally flawed without an equally rigorous way of authenticating the quality of a reconstruction to ensure it provides a reasonable representation of the data, given the known noise sources. A key motivation for developing such a tool is to enable experimentalists to rigorously diagnose the presence of technical noise in their tomographic data. In this work, I explore the performance of the chi-squared goodness-of-fit test statistic as a measure of reconstruction quality. I show that its behaviour deviates noticeably from expectations for states lying near the boundaries of physical state space, severely undermining its usefulness as a quantitative tool precisely in the region which is of most interest in quantum information processing tasks. I suggest a simple, heuristic approach to compensate for these effects and present numerical simulations showing that this approach provides substantially improved performance.
Entanglement is one of the most fascinating features of quantum theory, as it fundamentally distinguishes quantum systems from classical systems. It not only might play a role in natural processes, but provides an especially powerful resource for a plethora of quantum information protocols, including quantum state teleportation, superdense coding as well as quantum computation schemes. However, for larger systems involving more than two parties, it is a challenging task to verify and characterize entanglement. In this thesis, efficient means for detecting genuine multipartite entanglement in multiqubit quantum systems will be derived, demonstrated, and discussed. Beyond that, methods for quantum state and process tomography will be introduced, which allow to analyze and investigate prepared multipartite states or even the performance of whole setups. Some typical obstacles for reliable state tomography will be pointed out, together with new means to understand experimentally obtained data. Finally, the measurement problem, which describes the unavoidable backaction of a measurement process to the quantum state under investigation, will be illustrated. Together with the discussion of different methods of quantum measurements, the optimal measurement instruments for binary qubit measurements will be derived. These optimal measurement instruments allow to perform a quantum measurement, providing a tunable amount of information about the quantum state, while avoiding any unnecessary disturbance to the state. This set of optimal instruments will be compared to other measurement schemes, such as measurements based on the optimal quantum cloning protocol.
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.
Abstract Reliable verification of multipartite entanglement is a prerequisite for quantum information processing. However, the interplay between statistical fluctuations and systematic errors in Quantum State Tomography (QST) often obscures genuine quantum correlations. In this work, we perform a numerical benchmarking of QST performance for three-qubit GHZ and W states under a comprehensive noise model that incorporates Poissonian counting statistics, random unitary perturbations, white noise, and source instability. Beyond standard fidelity analysis, we utilize entanglement negativity and residual entanglement to investigate how these states respond to different noise sources. Our results highlight the response characteristics of entanglement measures and fidelity to experimental imperfections. We provide a quantitative analysis of the robustness profiles for both states, noting the entanglement decay and the evolution of residual entanglement under local unitary noise. Furthermore, we establish that employing an overcomplete tomographic set provides a slight advantage in mitigating systematic errors compared to standard informationally complete schemes. These findings provide a useful reference for analyzing the potential impacts of measurement artifacts and genuine decoherence in experimental setups.