Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement

Abstract

Quantum entanglement plays a central role in many areas of physics, from quantum information science to many-body systems. In order 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 most 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 nevertheless violate a Bell inequality. This shows that Bell nonlocality implies neither entanglement distillability, nor non-positivity under partial transposition, thus clarifying the relation between three fundamental aspects of entanglement. Finally, our results lead to a novel application of bound entanglement for device-independent randomness certification.

6 pages, 2 figure, 1 table

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• Quantitative bound entanglement in two-qutrit states
• A class of genuinely high-dimensionally entangled states with a positive partial transpose
• Catalytic and asymptotic equivalence for quantum entanglement
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• Quantum cloning of steering
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• Bound entangled states are useful in prepare-and-measure scenarios
• Bipartite Bound Entanglement
• Seven definitions of bipartite bound entanglement
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• Certifying nonlocal properties of noisy quantum operations
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Certifying the activation of Bell nonlocality with finite data
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• Local models and hidden nonlocality in Quantum Theory