论文标题
$ W $和Greenberger-Horne-Zeilinger的相互转换与横向全球控制的Ising耦合量子
Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
论文作者
论文摘要
$ W $的相互转换和Greenberger-Horne-Zeilinger州在各种物理系统中都引起了很大的关注。我们在具有远距离（全能）ISING-type Qubit-Qubit交互的Qubit阵列的相当通用的物理设置中解决了这个问题，这些相互作用同时由横向Zeeman-type全局控制字段作用。在某种程度上是由最近的谎言代数结果激励的，该结果暗示了这种系统对量子排列不变的任意状态的状态对状态的可控性，我们对三qubit案件中的状态内部转换问题进行了详细研究。所设想的互转换协议具有脉冲序列的形式，该序列由两个瞬时（三角形）控制脉冲组成，每个脉冲都与全局量子旋转相对应，以及它们之间有限持续时间的Ising Ictactiactiactiaction脉冲。它的构建在很大程度上依赖于三Q量的希尔伯特空间的（四维）置换不变的子空间（对称部门）。为了证明所提出的状态交换方案的生存能力，我们对基础脉冲序列对系统误差的鲁棒性进行了详细分析，即偏离其五个特征参数的最佳值。
Interconversions of $W$ and Greenberger-Horne-Zeilinger states in various physical systems are lately attracting considerable attention. We address this problem in the fairly general physical setting of qubit arrays with long-ranged (all-to-all) Ising-type qubit-qubit interaction, which are simultaneously acted upon by transverse Zeeman-type global control fields. Motivated in part by a recent Lie-algebraic result that implies state-to-state controllability of such a system for an arbitrary pair of states that are invariant with respect to qubit permutations, we present a detailed investigation of the state-interconversion problem in the three-qubit case. The envisioned interconversion protocol has the form of a pulse sequence that consists of two instantaneous (delta-shaped) control pulses, each of them corresponding to a global qubit rotation, and an Ising-interaction pulse of finite duration between them. Its construction relies heavily on the use of the (four-dimensional) permutation-invariant subspace (symmetric sector) of the three-qubit Hilbert space. In order to demonstrate the viability of the proposed state-interconversion scheme, we provide a detailed analysis of the robustness of the underlying pulse sequence to systematic errors, i.e. deviations from the optimal values of its five characteristic parameters.
