Institute for Nuclear Research, Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary.
Département de Physique Théorique, Université de Genève, 1211 Genève, Switzerland.
Nat Commun. 2014 Nov 5;5:5297. doi: 10.1038/ncomms6297.
Quantum entanglement has a central role in many areas of physics. To grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each other. In 1999, Peres conjectured that Bell nonlocality is equivalent to distillability of entanglement. The intuition of Peres was that the non-classicality of an entangled state, as witnessed via Bell inequality violation, implies that pure entanglement can be distilled from this state, hence making it useful for quantum information protocols. Subsequently, the Peres conjecture was shown to hold true in several specific cases, and became a central open question in quantum information theory. Here we disprove the Peres conjecture by showing that an undistillable bipartite entangled state--a bound entangled state--can violate a Bell inequality. Hence Bell nonlocality implies neither entanglement distillability, nor non-positivity under partial transposition. This clarifies the relation between three fundamental aspects of entanglement.
量子纠缠在物理学的许多领域中都起着核心作用。为了理解这一现象的本质，理解纠缠的不同表现形式之间的关系是至关重要的。1999 年，佩雷斯猜想贝尔非定域性等价于纠缠的可提取性。佩雷斯的直觉是，一个纠缠态的非经典性，通过违反贝尔不等式来证明，意味着可以从这个态中提取出纯纠缠，从而使其对量子信息协议有用。随后，在几个特定的情况下证明了佩雷斯猜想是正确的，并成为量子信息理论中的一个核心开放性问题。在这里，我们通过证明一个不可提取的双粒子纠缠态——束缚纠缠态——可以违反贝尔不等式，从而否定了佩雷斯猜想。因此，贝尔非定域性既不意味着纠缠可提取性，也不意味着部分转置下的非正定性。这就澄清了纠缠的三个基本方面之间的关系。
