Quantum state tomography with time-continuous measurements: reconstruction with resource limitations
Quantum state tomography with time-continuous measurements: reconstruction with resource limitations
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DOI：
10.1007/s40509-019-00198-2
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发表时间：
2018-05
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通讯作者：
Areeya Chantasri;Shengshi Pang;Teerawat Chalermpusitarak;A. Jordan
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作者：
Areeya Chantasri;Shengshi Pang;Teerawat Chalermpusitarak;A. Jordan
我们提出并分析了量子状态估计（层析成像）使用连续的量子测量与资源限制，允许许多量子比特的全局状态，仅从测量几个构造。我们给出了一个证明的原则调查证明成功的层析重建的任意初始量子态的三种不同的情况：单量子位，远程量子位，和两个相互作用的量子位。层析重建只利用一个连续的弱探针的一个单一的量子比特可观察的，一个固定的耦合哈密顿量，连同单量子比特控制。在单量子比特的情况下，一个可观测的连续测量和拉比振荡的组合足以找到所有三个未知的量子比特状态分量。对于两个相互作用的量子位，其中仅测量第一量子位的一个可观测量，可以实现控制哈密顿算子以经由量子位-量子位相互作用和局部应用于每个量子位的拉比振荡控制将所有量子信息转移到测量的可观测量。通过分析弱测量极限下的酉动力学和Fisher信息矩阵的估计，讨论了不同的控制集，并对层析结果进行了数值模拟。结果，我们得到了重建的状态的结晶度超过0.98与几千个测量运行。
We propose and analyze quantum state estimation (tomography) using continuous quantum measurements with resource limitations, allowing the global state of many qubits to be constructed from only measuring a few. We give a proof-of-principle investigation demonstrating successful tomographic reconstruction of an arbitrary initial quantum state for three different situations: single qubit, remote qubit, and two interacting qubits. The tomographic reconstruction utilizes only a continuous weak probe of a single qubit observable, a fixed coupling Hamiltonian, together with single-qubit controls. In the single-qubit case, a combination of the continuous measurement of an observable and a Rabi oscillation is sufficient to find all three unknown qubit state components. For two interacting qubits, where only one observable of the first qubit is measured, the control Hamiltonian can be implemented to transfer all quantum information to the measured observable, via the qubit–qubit interaction and Rabi oscillation controls applied locally on each qubit. We discuss different sets of controls by analyzing the unitary dynamics and the Fisher information matrix of the estimation in the limit of weak measurement, and simulate tomographic results numerically. As a result, we obtained reconstructed state fidelities in excess of 0.98 with a few thousand measurement runs.