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Local and Non-Local Invasive Measurements on Two Quantum Spins Coupled via Nanomechanical Oscillations
Symmetry ( IF 2.2 ) Pub Date : 2020-07-01 , DOI: 10.3390/sym12071078
Dimitrios Maroulakos , Levan Chotorlishvili , Dominik Schulz , Jamal Berakdar

Symmetry plays the central role in the structure of quantum states of bipartite (or many-body) fermionic systems. Typically, symmetry leads to the phenomenon of quantum coherence and correlations (entanglement) inherent to quantum systems only. In the present work, we study the role of symmetry (i.e., quantum correlations) in invasive quantum measurements. We consider the influence of a direct or indirect measurement process on a composite quantum system. We derive explicit analytical expressions for the case of two quantum spins positioned on both sides of the quantum cantilever. The spins are coupled indirectly to each others via their interaction with a magnetic tip deposited on the cantilever. Two types of quantum witnesses can be considered, which quantify the invasiveness of a measurement on the systems’ quantum states: (i) A local quantum witness stands for the consequence on the quantum spin states of a measurement done on the cantilever, meaning we first perform a measurement on the cantilever, and subsequently a measurement on a spin. (ii) The non-local quantum witness signifies the response of one spin if a measurement is done on the other spin. In both cases the disturbance must involve the cantilever. However, in the first case, the spin-cantilever interaction is linear in the coupling constant Ω , where as in the second case, the spin-spin interaction is quadratic in Ω . For both cases, we find and discuss analytical results for the witness.

中文翻译:

通过纳米机械振荡耦合的两个量子自旋的局部和非局部侵入测量

对称性在二分(或多体)费米子系统的量子态结构中起着核心作用。通常,对称性会导致量子系统固有的量子相干性和相关性(纠缠)现象。在目前的工作中,我们研究对称性(即量子相关性)在侵入性量子测量中的作用。我们考虑直接或间接测量过程对复合量子系统的影响。我们推导出两个量子自旋位于量子悬臂两侧的情况的明确解析表达式。自旋通过它们与沉积在悬臂上的磁性尖端的相互作用而间接地相互耦合。可以考虑两种类型的量子见证,它们量化了系统量子状态测量的侵入性:(i) 局部量子见证代表在悬臂上进行测量的量子自旋态的结果,这意味着我们首先对悬臂进行测量,然后对自旋进行测量。(ii) 如果在另一个自旋上进行测量,则非局部量子见证表示一个自旋的响应。在这两种情况下,扰动都必须涉及悬臂。然而,在第一种情况下,自旋 - 悬臂相互作用在耦合常数 Ω 中是线性的,而在第二种情况下,自旋 - 自旋相互作用在 Ω 中是二次的。对于这两种情况,我们都会找到并讨论证人的分析结果。(ii) 如果在另一个自旋上进行测量,则非局部量子见证表示一个自旋的响应。在这两种情况下,扰动都必须涉及悬臂。然而,在第一种情况下,自旋 - 悬臂相互作用在耦合常数 Ω 中是线性的,而在第二种情况下,自旋 - 自旋相互作用在 Ω 中是二次的。对于这两种情况,我们都会找到并讨论证人的分析结果。(ii) 如果在另一个自旋上进行测量,则非局部量子见证表示一个自旋的响应。在这两种情况下,扰动都必须涉及悬臂。然而,在第一种情况下,自旋 - 悬臂相互作用在耦合常数 Ω 中是线性的,而在第二种情况下,自旋 - 自旋相互作用在 Ω 中是二次的。对于这两种情况,我们都会找到并讨论证人的分析结果。
更新日期:2020-07-01
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