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两个大质量粒子的相对论纠缠

Relativistic entanglement of two massive particles

Nicolai Friis, Reinhold A. Bertlmann, Marcus Huber, Beatrix C. Hiesmayr

备注：
17 pages, 4 figures
发表信息：
Phys. Rev. A 81, 042114 (2010)
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摘要：

我们把两个大质量自旋- $\tfrac{1}{2}$粒子系统的自旋和动量自由度描述为一个4量子比特系统。然后，我们显式地显示了如何纠缠的变化之间的不同分区的量子比特，当考虑不同的惯性观测器。虽然两个粒子的纠缠对应于一个分区到爱丽丝和鲍勃的子系统是，正如文献中经常指出的，洛伦兹助推下不变，纠缠相对于其他分区的希尔伯特空间，另一方面，不是。它当然取决于所选择的惯性系和所考虑的初始状态。纠缠的变化出现了，因为洛伦兹对粒子动量的提升导致了自旋的维格纳旋转，在某些情况下，自旋与动量态纠缠在一起。我们系统地研究了不同类型的初始自旋状态和不同的分区的4量子比特空间的情况。此外，我们研究了贝尔不等式的行为，不同的观察者和演示如何最大可能程度的违反，使用保利-鲁班斯基自旋可观察，可以恢复任何惯性观察者。

英文摘要：

We describe the spin and momentum degrees of freedom of a system of two massive spin--$\tfrac{1}{2}$ particles as a 4 qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin- with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the 4 qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.

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