对玻色高斯集合的测量相当精确

IF 0.7 4区 物理与天体物理 Q3 COMPUTER SCIENCE, THEORY & METHODS International Journal of Quantum Information Pub Date : 2024-05-25 DOI:10.1142/s0219749924400100
Hemant K. Mishra, Ludovico Lami, Prabha Mandayam, Mark M. Wilde
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引用次数: 0

摘要

相当好测量是量子信息论中的一个基本分析工具,它提供了一种推断经典标签的方法,该标签可识别从集合中概率选择的量子态。识别和构建玻色高斯态的 "相当好测量 "对量子信息处理任务具有直接的实际意义。Holevo 最近证明,玻色高斯集合的相当好测量是一种玻色高斯测量,它能获得集合的可获取信息 [IEEE Trans. Inf. Theory66(9) (2020) 5634]。在本文中,我们为多模玻色态高斯集合的相当好测量提供了另一种高斯性证明,重点是建立测量的显式和高效可计算的高斯描述。我们还计算了相当好测量的均方误差的显式形式,这在使用它进行参数估计时非常重要。我们证明,如果输入状态是忠实的高斯状态,其协方差矩阵满足一定条件,那么漂亮仪器的测量后状态就是忠实的高斯状态。结合我们之前对 "相当好 "测量的发现,如果同样的条件成立,那么预期输出状态也是一个忠实的高斯状态。在这种情况下,我们计算出测量后和预期输出状态的明确高斯描述。我们的发现意味着玻色高斯集合的相当好仪器不再仅仅是一个分析工具,它也可以在量子光学实验室中实验性地实现。
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Pretty good measurement for bosonic Gaussian ensembles

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation.

Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.

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来源期刊
International Journal of Quantum Information
International Journal of Quantum Information 物理-计算机:理论方法
CiteScore
2.20
自引率
8.30%
发文量
36
审稿时长
10 months
期刊介绍: The International Journal of Quantum Information (IJQI) provides a forum for the interdisciplinary field of Quantum Information Science. In particular, we welcome contributions in these areas of experimental and theoretical research: Quantum Cryptography Quantum Computation Quantum Communication Fundamentals of Quantum Mechanics Authors are welcome to submit quality research and review papers as well as short correspondences in both theoretical and experimental areas. Submitted articles will be refereed prior to acceptance for publication in the Journal.
期刊最新文献
Low-ground/High-ground capacity regions analysis for bosonic gaussian channels Interpreting symplectic linear transformations in a two-qubit phase space Continuity of the relative entropy of resource Alexander S. Holevo’s researches in quantum information theory in 20th century Pretty good measurement for bosonic Gaussian ensembles
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