Activation of Nonlocality in Bound Entanglement

We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully biseparable three-qubit bound entangled state with a local model for the most general (nonsequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters are applied. Our results demonstrate the first example of activation of nonlocality in bound entanglement. Hence, we show that genuine hidden nonlocality does not imply entanglement distillability.

Figure 1

Abstract overview of our results. We show that the set of nonlocal bound entangled states (BE states) can be enlarged in the hidden nonlocality scenario (HNL). This is the first step towards a possible equivalence of all BE states and all nonlocal BE states. Further enlargements of the set of nonlocal BE states could be provided by superactivation (SA) and the asymptotic scenario (Asymp.), similar to the case for distillable states. It is also an open question, whether the set can be enlarged to all BE states in such scenarios.

Figure 2

Schematic overview over the relevant sets of states. The states in the shaded area are undistillable. Our results confirm the existence of bound entangled states with an LHV for POVMs. However, (invertible) local filters $F$ are able to reveal the hidden nonlocality of these states. They map a state ${\rho }_L$ from the set of states admitting an LHV onto a nonlocal state ${\rho }_{\mathrm{NL}}$.