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Privacy in Networks of quantum Sensors

Physical Review Letters 2025年第3期134卷 030802-030802页

作者： Majid Hassani Santiago Scheiner Matteo G. A. Paris Damian Markham LIP6 CNRS Sorbonne Université 4 place Jussieu F-75005 Paris France Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands ⟨aQa⟩Applied Quantum Algorithms Leiden The Netherlands Quantum Technology Lab Università degli Studi di Milano I-20133 Milano Italy

We treat privacy in a network of quantum sensors where accessible information is limited to specific functions of the network parameters, and all other information remains private. We develop an analysis of privacy in terms of a manipulation of the quantum Fisher information matrix, and find the optimal state achieving maximum privacy in the estimation of linear combination of the unknown parameters in a network of quantum sensors. We also discuss the effect of uncorrelated noise on the privacy of the network. Moreover, we illustrate our results with an example where the goal is to estimate the average value of the unknown parameters in the network. In this example, we also introduce the notion of quasiprivacy (ε privacy), quantifying how close the state is to being private.

关键词： Differential privacy

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Analyzing Prospects for quantum Advantage in Topological Data Analysis

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PRX quantum 2024年第1期5卷 010319-010319页

作者： Dominic W. Berry Yuan Su Casper Gyurik Robbie King Joao Basso Alexander Del Toro Barba Abhishek Rajput Nathan Wiebe Vedran Dunjko Ryan Babbush School of Mathematical and Physical Sciences Macquarie University Sydney NSW 2109 Australia Google Quantum AI Venice California 90291 USA applied Quantum algorithms (aQa) Leiden University Leiden 2300 RA Netherlands Department of Computing and Mathematical Sciences Caltech Pasadena California 91125 USA Department of Computer Science University of Toronto Ontario M5S 2E4 Canada Pacific Northwest National Laboratory Richland Washington 99354 USA

Lloyd et al. [Nat. Commun. 7, 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances.

关键词： quantum algorithms & computation

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Randomness versus Nonlocality in Multiple-Input and Multiple-Output quantum Scenario

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Physical Review Letters 2025年第9期134卷 090201-090201页

作者： Chao Zhang Yi Li Xiao-Min Hu Yu Xiang Chuan-Feng Li Guang-Can Guo Jordi Tura Qihuang Gong Qiongyi He CAS Key Laboratory of Quantum Information University of Science and Technology of China Hefei 230026 China CAS Synergetic Innovation Center of Quantum Information and Quantum Physics University of Science and Technology of China Hefei 230026 China State Key Laboratory for Mesoscopic Physics School of Physics Frontiers Science Center for Nano-optoelectronics and Collaborative Innovation Center of Quantum Matter Peking University Beijing 100871 China Beijing Academy of Quantum Information Sciences Beijing 100193 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi 030006 China ⟨aQa⟩ Applied Quantum Algorithms Leiden The Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands Peking University Yangtze Delta Institute of Optoelectronics Nantong Jiangsu 226010 China Hefei National Laboratory Hefei 230088 China

Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices, thus provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for generating quantum randomness, but the minimal resource required has not been clarified. Here we prove and experimentally demonstrate that violating any two-input Bell inequality is both necessary and sufficient for certifying randomness, however, for the multiple-input cases, this sufficiency ceases to apply, leading to certain states exhibiting Bell nonlocality without the capability to certify randomness. We examine two typical classes of Bell inequalities with multiple input and multiple output, the facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities, in the high-dimensional photonic system, and observe that the violation of the latter one can always certify randomness which is not true for the former. The private randomness with a generation rate of 1.867±0.018 bits per photon pair is obtained in the scenario of Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities with 3-input and 4-output. Our Letter unravels the internal connection between randomness and nonlocality, effectively enhancing the performance of tasks such as device-independent random number generation.

关键词： Random number generation

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Probing Many-Body Bell Correlation Depth with Superconducting Qubits

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Physical Review X 2025年第2期15卷 021024-021024页

作者： Ke Wang Weikang Li Shibo Xu Mengyao Hu Jiachen Chen Yaozu Wu Chuanyu Zhang Feitong Jin Xuhao Zhu Yu Gao Ziqi Tan Zhengyi Cui Aosai Zhang Ning Wang Yiren Zou Tingting Li Fanhao Shen Jiarun Zhong Zehang Bao Zitian Zhu Zixuan Song Jinfeng Deng Hang Dong Xu Zhang Pengfei Zhang Wenjie Jiang Zhide Lu Zheng-Zhi Sun Hekang Li Qiujiang Guo Zhen Wang Patrick Emonts Jordi Tura Chao Song H. Wang Dong-Ling Deng School of Physics ZJU-Hangzhou Global Scientific and Technological Innovation Center and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control Zhejiang University Hangzhou 310027 China Center for Quantum Information IIIS Tsinghua University Beijing 100084 China Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands ⟨aQa⟩ Applied Quantum Algorithms Leiden The Netherlands Shanghai Qi Zhi Institute Shanghai 200232 China Hefei National Laboratory Hefei 230088 China

quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications.

关键词： Qubits

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Mitigating shot noise in local overlapping quantum tomography with semidefinite programming

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Physical Review A 2025年第5期111卷 052444-052444页

作者： Zherui Jerry Wang David Dechant Yash J. Patel Jordi Tura 〈aQa〉 Applied Quantum Algorithms Universiteit Leiden The Netherlands Instituut-Lorentz Universiteit Leiden P.O. Box 9506 2300 RA Leiden The Netherlands QuTech Delft University of Technology P.O. Box 5046 Delft 2600 GA The Netherlands LIACS Universiteit Leiden Niels Bohrweg 1 2333 CA Leiden The Netherlands

Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum states. In the context of near-term quantum computing, RDMs provide sufficient information to effectively design variational quantum algorithms. However, their experimental estimation is challenging, as it involves preparing and measuring quantum states in multiple bases, a resource-intensive process susceptible to producing nonphysical RDMs due to shot noise from limited measurements. To address this, we propose a method to mitigate shot noise by reenforcing certain physicality constraints on RDMs. While verifying RDM compatibility with a global state is quantum Merlin-Arthur complete, we relax this condition by enforcing compatibility constraints up to a certain level using a polynomial-size semidefinite program to reconstruct overlapping RDMs from simulated data. Our approach yields, on average, tighter bounds for the same number of measurements compared to tomography without compatibility constraints. We demonstrate the versatility and efficacy of our method by integrating it into an algorithmic cooling procedure to prepare low-energy states of local Hamiltonians. Simulations on frustrated Hamiltonians reveal notable improvements in accuracy and resource efficiency, highlighting the potential of our approach for practical applications in near-term quantum computing.

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