Bell inequality, separability and entanglement distillation

Marian Kupczyński

Liming, Shao-Ming, Li-Jost +1 more

在这评论，我们介绍著名贝尔不平等，在钟不平等之间的关系和量可分性，和量状态的纠纷蒸馏。任何纯纠缠的量状态违背钟形的不平等之一，这被显示出。而且，违背任何一这些钟形的不平等的量状态被显示可由蒸馏而得。检测更多的纠缠的混合状态的新贝尔不平等也被介绍。

Firouz Amiri, Shahpoor Moradi

Entanglement of tripartite spin states under Lorentz transformations is studied in the context of Bell’s inequality and positive partial transpose criterion. First the relativistic analogue of Bell’s inequality is discussed for three qubit states by explicit calculation of the Wigner rotation. We use the relativistic invariant spin operator which is related to the Pauli-Lubanski pseudo vector. For observers at rest the Bell’s inequality is speed-independent and maximally violated. For moving observers it’s shown that Bell’s inequality is violated and the amount of violation depends on the boost speed. We show that in ultrarelativistic limit Bell’s inequality is still maximally violated. We also obtained the critical value for satisfying Bell’s inequality. The critical value of boost speed for violation of inequality for particles moving in the center of mass frame is greater than that for particles moving with the same momentum. Second we investigate the entanglement distillability of tripartite mixed spin states under Lorentz transformations in the context of Werner states. We show that there are states that will change from distillable (entangled) into separable for a certain value of rapidity.

Antonio Acín

We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, Dür [Phys. Rev. Lett. 87, 230402 (2001)] has shown that there are some multiparticle bound entangled states which are nonseparable and nondistillable, that violate a Bell inequality. We prove that for all the states violating this inequality there exists at least one splitting of the parties into two groups such that some pure-state entanglement can be distilled, obtaining a connection between Bell inequalities and bipartite distillable entanglement.

Biao Wu