Conditional steering under the von Neumann scenario

Mukherjee, Kaushiki; Paul, Biswajit; Karmakar, Sumana; Sarkar, Debasis; Mukherjee, Amit; Bhattacharya, Some Sankar; Roy, Arup

doi:10.1103/physreva.96.022122

Cited by 6 publications

(7 citation statements)

References 78 publications

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“…In a network scenario each source typically connects to a proper subset of parties in contrast to the standard Bell scenario. Independence of sources in quantum networks adds * kaushiki.wbes@gmail.com new physical insights in analyzing non classicality of network correlations [1,10,11,[13][14][15][16][17][18][19][20][21][22][23][24][25]. For instance consider the simplest network of three parties, Alice (A), Bob (B) and Charlie (C), and two independent sources S 1 , S 2 .…”

Section: Introductionmentioning

confidence: 99%

“…Under suitable measurement choices, nonbilocal tripartite correlations may be shared at the end of the experiment. over time, the bilocal network has been generalized on basis of various factors such as increasing number of parties, sources [14,18], a pattern of arranging independent sources and parties [13], etc. Quantum network structures with independent sources are compatible with repeater networks [5,33], where entanglement gets distributed via the entanglement swapping procedure among initially uncorrelated nodes.…”

Section: Introductionmentioning

confidence: 99%

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Detecting Nontrilocal Correlations In Triangle Networks

Mukherjee

2023

Preprint

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Correlations in quantum networks with independent sources exhibit a completely novel form of nonclassicality in the sense that the nonlocality of such correlations can be demonstrated in fixed local input scenarios. Before the pioneering work by M. O.Renou, et al.,in [1], the nonlocal feature of such network correlations was directly attributable to standard Bell nonlocality. In [1], the authors provided some of the first examples of triangle network correlations, whose nonlocality cannot be deduced from Bell-CHSH nonlocality. To date, a complete characterization of such scenarios is yet to be provided. Present work characterizes correlations arising due to fixed local measurements in a triangle network under a source independence assumptions. Precisely speaking, a set of criteria is framed in the form of Bell-type inequalities, each of which is necessarily satisfied by trilocal correlations. Possible quantum violation of at least one criterion from the set is analyzed, which in turn points out the utility of the set of criteria to detect nonlocality (nontrilocality) in quantum triangle networks. Interestingly, measurement on a local product state basis turns out to be sufficient to generate nontrilocal correlations in some quantum networks. Noise tolerance of the detection criteria is discussed followed by a generalization of the framework for demonstrating correlations in any n-sided polygon where n is finite.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Detecting Nontrilocal Correlations In Triangle Networks

Mukherjee

2023

Preprint

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“…This is also in contrast to the standard Bell scenario, where the random and free choice of inputs by each party is crucial to demonstrate Bell nonlocality. Different research activities have been conducted which provide for the characterization of quantum correlations in n-local networks [13][14][15][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Much like the usual Bell nonlocality experiments, violation of an nlocal inequality indicates the presence of n-nonlocal correlations.…”

Section: Introductionmentioning

confidence: 99%

Hidden Non n-locality In Linear Networks

Mukherjee¹,

Mandal²,

Patro³

et al. 2023

Preprint

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We study here a hitherto unexplored line of research, namely an investigation which reveals 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 non bilocality and non trilocality, where we notice quite intriguingly that non bilocality is observed even when one of the sources distributes a mixed two-qubit separable state. Furthermore a characterization of hidden non bilocality is also provided in terms of the Bloch-Fano decomposition, wherein we conjecture that to witness hidden non bilocality, one of the two states (used by the sources) must have non-null Bloch vectors.

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“…[ 19 ] The experimental test of quantum violations of various bilocality and n ‐locality inequalities in star‐network configuration have been reported. [ 36–58 ]…”

Section: Introductionmentioning

confidence: 99%

Optimal Quantum Violations of n‐Locality Inequalities with Conditional Dependence on Inputs

Munshi

Pan

2023

Annalen der Physik

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Bell experiment in a network gives rise to a form of quantum nonlocality which is conceptually different from traditional multipartite Bell nonlocality. In this work, the star‐network configuration involving arbitrary n independent sources and false(n+1false)$(n+1)$ parties, including n edge parties and one central party is considered. Each of the n edge parties shares a physical system with the central party. Each edge party receives 2m−1$2^{m-1}$ number of inputs, and the central party receives an arbitrary m number of inputs. The conditional dependence on the inputs of each edge party is imposed so that the local probabilities satisfy a set of constraints. A family of generalized n‐locality inequalities is proposed in the arbitrary input scenario by imposing the set of constraints on inputs. The optimal quantum violation of the inequalities is derived by using an elegant sum‐of‐squares approach without specifying the dimension of the quantum system. Notably, the optimal quantum value is achieved only when the set of linear constraints on inputs is satisfied, which, in turn, self‐tests the observables required for each edge party. It shows that while conditional dependence on inputs significantly reduces the n‐local bound of the inequalities, the optimal quantum violation remains invariant. It argues that this implies a more robust test of network non‐locality, which can be revealed for smaller visibility parameters of the corresponding state. Further, the network nonlocality is characterized and examine its correspondence with suitably derived standard Bell nonlocality.

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Conditional steering under the von Neumann scenario

Cited by 6 publications

References 78 publications

Detecting Nontrilocal Correlations In Triangle Networks

Detecting Nontrilocal Correlations In Triangle Networks

Hidden Non n-locality In Linear Networks

Optimal Quantum Violations of n‐Locality Inequalities with Conditional Dependence on Inputs

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