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.
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.
The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states that admit a fully local hidden variable model, i.e., where all parties are separated. Hence, although these states exhibit the strongest form of multipartite entanglement, they cannot lead to Bell inequality violation considering general nonsequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely, projective measurements. Here, we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements, and show that the states violate a Bell inequality after local filtering. Hence, there exist entangled states, the nonlocality of which can be revealed only by using a sequence of measurements. Finally, we show that genuine hidden nonlocality can be maximal. There exist entangled states for which a sequence of measurements can lead to maximal violation of a Bell inequality, while the statistics of nonsequential measurements is always local.
Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state: ρα=α|Φ+⟩⟨Φ+|+(1−α)14. We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12 , in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.
Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality. A central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and show that the test can be implemented by semidefinite programing. This method can be applied to any given state and for the construction of new examples of states with local hidden variable models for both projective and general measurements. As applications, we provide a lower-bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those that arise from physical noise models, Bell-diagonal states, and noisy Greenberger-Horne-Zeilinger and W states.