论文标题
通过Pauli测量样品有效断层扫描
Sample efficient tomography via Pauli Measurements
论文作者
论文摘要
保利测量是量子信息科学的理论和实验方面中最重要的测量。在本文中，我们探讨了保利测量在与州断层扫描有关的问题中的力量。首先，我们证明可以使用$ {\ Mathcal {o}}（\ frac {10^n} {10^n} {ε^2}）$使用Pauli Suesurements的副本来实现$ n $ qubit系统的\ textIt {量子状态层析成像}问题。作为一个直接应用程序，我们研究了Cotler和Wilczek在Ref中引入的\ textit {Quantit {Quantit重叠断层扫描}问题。 \ cite {cotler_2020}。 We show that the sample complexity is $\mathcal{O}(\frac{10^k\cdot\log({{n}\choose{k}}/δ))}{ε^{2}})$ for quantum overlapping tomography of $k$-qubit reduced density matrices among $n$ is quantum system, where $1-δ$ is the confidential level, $ε$是跟踪距离错误。这可以使用Pauli测量结果来实现。此外，我们证明需要$ω（\ frac {\ log（n/δ）} {ε^{2}}）$副本。换句话说，对于常数$ k $，联合，高度纠缠，测量值在渐近上比Pauli的测量更有效。
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly, we show that the \textit{quantum state tomography} problem of $n$-qubit system can be accomplished with ${\mathcal{O}}(\frac{10^n}{ε^2})$ copies of the unknown state using Pauli measurements. As a direct application, we studied the \textit{quantum overlapping tomography} problem introduced by Cotler and Wilczek in Ref. \cite{Cotler_2020}. We show that the sample complexity is $\mathcal{O}(\frac{10^k\cdot\log({{n}\choose{k}}/δ))}{ε^{2}})$ for quantum overlapping tomography of $k$-qubit reduced density matrices among $n$ is quantum system, where $1-δ$ is the confidential level, and $ε$ is the trace distance error. This can be achieved using Pauli measurements. Moreover, we prove that $Ω(\frac{\log(n/δ)}{ε^{2}})$ copies are needed. In other words, for constant $k$, joint, highly entangled, measurements are not asymptotically more efficient than Pauli measurements.
