基于泡利测量的量子混合度测试
Near-Optimal Mixedness Testing with Pauli Measurements
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中文总结 AI 辅助
该研究针对N量子比特态的混合度测试问题，提出随机泡利基测量协议，给出单量子比特混合度测试的样本量结论，为量子态认证提供新的测量依赖下界框架。
中文摘要 AI 辅助
我们研究混合度测试这一基础问题：给定N量子比特态ρ的n份副本，以高概率判定ρ是否为最大混态（即ρ=𝕀_d/d，其中d=2^N），或满足‖ρ−𝕀_d/d‖₁≥ε。我们聚焦于单量子比特测量的实用场景，这类测量对每个量子比特独立制备。我们给出单量子比特混合度测试的近乎完整结论，证明所需样本量n=Θ̃(√10^N/ε²)。为建立下界，我们提出一种新的依赖测量的自适应单副本态认证下界框架；为建立上界，我们给出一种随机泡利基测量协议，该协议依赖于布尔超立方体上相关集中分布的计算高效均匀性测试新原语。
英文摘要
We consider a fundamental problem of \emph{mixedness testing}: Given $n$ copies of an $N$-qubit state $ρ$, determine whether $ρ= \mathbb{I}_d/d$ or $\|ρ-\mathbb{I}_d/d\|_1 \geq \varepsilon$ with high probability, where $d = 2^N$. In particular, we focus on performing this task in the practical setting of single-qubit measurements, where measurements are prepared independently on each qubit. We provide a nearly complete picture of single-qubit mixedness tesing by showing $n = \tildeΘ\left(\sqrt{10}^N/\varepsilon^2\right)$. To establish our lower bound, we introduce a measurement-dependent lower bound framework for adaptive single-copy state certification. For the upper bound, we present a randomized Pauli basis measurement protocol, which relies on a new primitive for computationally efficient uniformity testing of correlation-concentrated distributions on the Boolean hypercube. In conjunction, we provide lower and upper bounds for mixedness testing with fixed Pauli measurement protocols.
发表机构
- Cornell University（康奈尔大学）
- Rice University（莱斯大学）
- Stony Brook University（石溪大学）
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