通过埃尔米特守恒图的幂模拟非完全正动作

IF 6.6 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Fuchuan Wei, Zhenhuan Liu, Guoding Liu, Zizhao Han, Dong-Ling Deng, Zhengwei Liu
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引用次数: 0

摘要

合法的量子运算必须遵守量子力学的原则,特别是完全正性和痕迹保存的要求。然而,非完全正映射,特别是保持埃尔米特映射,在量子信息科学中起着至关重要的作用。在这里,我们引入了Hermitian-preserving map的幂运算算法,该算法可以通过将任意Hermitian-preserving map的输出\({\mathcal{N}}(\rho )\)幂运算为量子过程\({e}^{-i{\mathcal{N}}(\rho )t}\)来有效地模拟其作用。我们分析了该算法的样本复杂度,并在某些情况下证明了它的最优性。与基于单拷贝操作的协议相比,该算法利用正映射(但不是完全正映射)提供了指数级的纠缠检测和量化速度。此外,该方法通过模拟噪声信道的逆映射,实现了从多个噪声量子态中无噪声量子态的免编码恢复,为处理量子噪声提供了一种新的方法。该算法作为大规模量子算法的构建块,并为在广泛的信息处理任务中探索潜在的量子加速提供了途径。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Simulating non-completely positive actions via exponentiation of Hermitian-preserving maps

Simulating non-completely positive actions via exponentiation of Hermitian-preserving maps

Legitimate quantum operations must adhere to principles of quantum mechanics, particularly the requirements of complete positivity and trace preservation. Yet, non-completely positive maps, especially Hermitian-preserving maps, play a crucial role in quantum information science. Here, we introduce the Hermitian-preserving map exponentiation algorithm, which can effectively simulate the action of an arbitrary Hermitian-preserving map by exponentiating its output, \({\mathcal{N}}(\rho )\), into a quantum process, \({e}^{-i{\mathcal{N}}(\rho )t}\). We analyze the sample complexity of this algorithm and prove its optimality in certain cases. Utilizing positive but not completely positive maps, this algorithm provides exponential speedups in entanglement detection and quantification compared to protocols based on single-copy operations. In addition, it facilitates the encoding-free recovery of noiseless quantum states from multiple noisy ones by simulating the inverse map of the corresponding noise channel, providing a new approach to handling quantum noises. This algorithm acts as a building block of large-scale quantum algorithms and presents a pathway for exploring potential quantum speedups across a wide range of information-processing tasks.

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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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