arXiv 2103.077442021-03-13quant-ph

中、超相对论体系中的单粒子纠缠

Single particle entanglement in the mid-and ultra-relativistic regime

M. Ondra, B. C. Hiesmayr

备注：: 9 pages, 3 figures
发表信息：: Journal of Physics A: Mathematical and Theoretical (2021)
DOI：: 10.1088/1751-8121/ac2548

摘要：

在这项工作中，我们分析了纠缠量与自旋和动量自由度的一个大质量的自旋$\frac{1}{2}$粒子从相对论的角度来看。洛仑兹推进的效应引入了维格纳旋转，它将自旋和动量自由度关联起来。我们表明，自然的基础上讨论的几何效应的提升是螺旋度本征态在休息帧。在中等相对论性区域（Wigner旋转角受$δ< \fracπ{2}$限制），我们证明了对于具有相等螺旋度的态，纠缠度随Wigner旋转角单调减小，而在超相对论性区域（$δ> \fracπ{2}$），纠缠度随Wigner旋转角增大.如果准备的状态作为一个不相等的螺旋度本征态的叠加，单调的行为是颠倒的。这意味着，在超相对论制度的几何设置，可以找到这样的纠缠量表现出局部最大值或最小值。这表明了一个反直觉的行为的相对量的纠缠，由于内部和外部的几何配置空间的影响，并指向在实现洛伦兹不变的纠缠一般制定的困难。

英文摘要：

In this work we analyze the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin-$\frac{1}{2}$ particle from a relativistic perspective. The effect of a Lorentz boost introduces a Wigner rotation that correlates the spin and momentum degrees of freedom. We show that the natural basis to discuss the geometrical effects of the boost are the helicity eigenstates in the rest frame. In the mid-relativistic regime (where the Wigner rotation angle is limited by $δ< \fracπ{2}$) we prove for states with equal helicity that the entanglement with respect to the Wigner rotation angle is monotonically decreasing, however, in the ultra-relativistic regime ($δ> \fracπ{2}$) the entanglement is increasing. If the states are prepared as a superposition of unequal helicity eigenstates, the monotonic behaviour is inverted. This implies that in the ultra-relativistic regime a geometrical setup can be found such that the amount of entanglement exhibits local maxima or minima. This shows a counter-intuitive behaviour of the relative amount of entanglement, an effect due to the internal and external geometrical configuration space, and points towards the difficulties in achieving a Lorentz invariant formulation of entanglement in general.

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