Keeping pace with technological advancement, in the past decade, use of scalable networks have extended the study of quantum non-classicality beyond the regime of Bell-CHSH nonlocality. Present work provide characterization of non n-locality that can be exploited by incorporating filtering operations in star-shaped n-local networks. This in turn provide a framework of sequential n-local networks capable of generating non n-local correlations by involving some suitable form of stochastic local operations assisted with classical communications(SLOCC). It is observed that for effectiveness of such sequential networks, Bell-CHSH nonlocality(upto SLOCC operations) of every individual two-qubit state, distributed in the network, is not mandatory. However, there does not exist any separable local filter, which when applied in n-local network involving only Bell local states(upto SLOCC operations), can reveal non n-locality. Interestingly, instances revealing advantage of nonseparable mutli-qubit local filters over separable mutli-qubit local filters(by central node) are obtained. Such an advantage is attributable to the specific topology of star-shaped n-local networks and thus can never be reflected in Bell scenario.
Keeping pace with technological advancement, in the past decade, use of scalable networks have extended the study of quantum non-classicality beyond the regime of Bell-CHSH nonlocality. Present work provide characterization of non n-locality that can be exploited by incorporating filtering operations in star-shaped n-local networks. This in turn provide a framework of sequential n-local networks capable of generating non n-local correlations by involving some suitable form of stochastic local operations assisted with classical communications(SLOCC). It is observed that for effectiveness of such sequential networks, Bell-CHSH nonlocality(upto SLOCC operations) of every individual two-qubit state, distributed in the network, is not mandatory. However, there does not exist any separable local filter, which when applied in n-local network involving only Bell local states(upto SLOCC operations), can reveal non n-locality. Interestingly, instances revealing advantage of nonseparable mutli-qubit local filters over separable mutli-qubit local filters(by central node) are obtained. Such an advantage is attributable to the specific topology of star-shaped n-local networks and thus can never be reflected in Bell scenario.
We study hidden nonlocality in a linear network with independent sources. In the usual paradigm of Bell nonlocality, there are certain states which exhibit nonlocality only after the application of suitable local filtering operations, which, in turn, are some special stochastic local operations assisted with classical communication (SLOCC). In the present work, we introduce the notion of hidden non n-locality. The notion is detailed using a bilocal network. We provide instances of hidden nonbilocality and nontrilocality, where we notice quite intriguingly that nonbilocality is observed even when one of the sources distributes a mixed two-qubit separable state. Furthermore, a characterization of hidden nonbilocality is also provided in terms of the Bloch-Fano decomposition, wherein we conjecture that, to witness hidden nonbilocality, one of the two states (used by the sources) must have nonnull local Bloch vectors. Noise is inevitable in practical scenarios, which makes it imperative to study any possible method to enhance the possibility of detecting nonclassicality in the presence of noise in the network. We find that local filtering enhances the robustness to noise, which we demonstrate using bit-flip and amplitude-damping channels.
The launch of a satellite capable of distributing entanglement through long distances and the first loophole-free violation of Bell inequalities are milestones indicating a clear path for the establishment of quantum networks. However, nonlocality in networks with independent entanglement sources has only been experimentally verified in simple tripartite networks, via the violation of bilocality inequalities. Here, by using a scalable photonic platform, we implement star-shaped quantum networks consisting of up to five distant nodes and four independent entanglement sources. We exploit this platform to violate the chained n-locality inequality and thus witness, in a device-independent way, the emergence of nonlocal correlations among the nodes of the implemented networks. These results open new perspectives for quantum information processing applications in the relevant regime where the observed correlations are compatible with standard local hidden variable models but are non-classical if the independence of the sources is taken into account.
Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to the standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non-n-locality in two distinct network topologies (linear and star). We have studied the extremal violations of n-local inequalities (compatible with linear and star network) for any fixed amount of entanglement (in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non-n-locality in a linear network. However, the same is not true for star n-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-n-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the n-local inequalities is also provided. Interestingly, detection of non-n-locality is ensured in the network if product of concurrence of all the sources involved exceeds 21.
Analyzing the nonclassicality of correlations generated in n-local quantum networks is an important branch of study in quantum information theory. Speaking of nonclassicality, violation of an n-local inequality ensures non n-locality of corresponding network correlations. Being correlation-based, violation of any such inequality is experimentally feasible. The present work explores whether applying suitable local unitary operations can aid violation of any n-local inequality. Observations have ensured the utility of local unitary operations in enhancing the detection efficiency of bilocal inequality and n-local inequality (for n=3,4) in the star configuration. In an n-local quantum network, such operations correspond to local basis change applied by at least one party over its joint state of qubits received from the sources. In an n-local network, with all the parties performing any possible local unitary operation, correlations not violating an n-local inequality (compatible with the network considered), are first characterized. Such characterization is then exploited to provide examples of local unitary operations aiding violation of existing n-local inequalities for n=2, 3, and 4, specifically. Interestingly, there exist two qubit unitary operations, for which nontrilocal correlations can be simulated even when one of the sources distribute pure product state in star network. Quantum gates associated with the useful unitary operations are provided.
Abstract The correlations in quantum networks have attracted strong interest due to the fact that linear Bell inequalities derived from one source are useless for characterizing multipartite correlations of general quantum networks. In this paper, a type of multi-star-shaped quantum networks are introduced and discussed. Such a network consists of three-grade nodes: the first grade is named party (node) A , the second one consists of m nodes marked B 1 , B 2 , …, B m , which are stars of A and the third one consists of m 2 nodes C k j ( j , k = 1 , 2 , … , m ) , where C k j ( k = 1 , 2 , … , m ) are stars of B j . We call such a network a three-grade m -star quantum network and denoted by SQN (3, m ), being as a natural extension of bilocal networks and star-shaped networks. We introduce and discussed the locality and strong locality of a SQN (3, m ) and derive the related nonlinear Bell inequalities, called (3, m )-locality inequalities and (3, m )-strong locality inequalities. To compare with the bipartite locality of quantum states, we define the separability of SQN (3, m ) that imply the locality and then locality of SQN (3, m ). When all of the shared states of the network are pure ones, we prove that SQN (3, m ) is nonlocal if and only if it is entangled.
Of late, there has been an upsurge of interest in studying the sequential sharing of various forms of quantum correlations, viz., nonlocality, preparation contextuality, coherence, and entanglement. In this work, we explore the sequential sharing of nonlocality in a quantum network. We first consider the simplest case of the two-input bilocality scenario that features two independent sources and three parties, including two edge parties and a central party. We demonstrate that, in the symmetric case when the sharing is considered for both the edge parties, the nonlocality can be shared by, at most, two sequential observers per edge party. However, in the asymmetric case, when the sharing across one edge party is considered, we show that, at most, six sequential observers can share the nonlocality in the network. We extend our investigation to the two-input n-local scenario in the star-network configuration that features an arbitrary n number of edge parties and one central party. In the asymmetric case, we demonstrate that the network nonlocality can be shared by an unbounded number of sequential observers across one edge party for a suitably large value of n. Further, we generalize our study for an arbitrary m input n-local scenario in the star-network configuration. We show that, even for an arbitrary m input scenario, the nonlocality can be shared by an unbounded number of sequential observers. However, increasing the input m, one has to employ a larger number of edge parties n than that of the two-input case to demonstrate the sharing of an unbounded number of sequential observers.