Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Hansenne, Kiara; Xu, Zhen-Peng; Kraft, Tristan; Gühne, Otfried

doi:10.1038/s41467-022-28006-3

Cited by 26 publications

(11 citation statements)

References 50 publications

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“…On the one hand they may lead to forbidden correlation structures that the underlying fiber network simply cannot create as in, e.g. [483] and as mentioned above. On the other hand one may conclude that in fact even a physical chain suffices for the creation of a variety of entanglement networks such as lattices, random networks and small-world networks [484].…”

Section: Entanglement Distribution: Prerequisite For Quantum Informat...mentioning

confidence: 99%

Complex quantum networks: a topical review

Nokkala,

Piilo,

Bianconi

2024

J. Phys. A: Math. Theor.

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These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is ﬂourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising ﬁeld of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer signiﬁcant complex network properties. The ﬁeld features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that uniﬁes the ﬁeld of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.

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Section: Entanglement Distribution: Prerequisite For Quantum Informat...mentioning

confidence: 99%

Complex quantum networks: a topical review

Nokkala,

Piilo,

Bianconi

2024

J. Phys. A: Math. Theor.

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“…Regarding the fixed input scenario, only a few particular instances of quantum nontrilocal correlations exist in a triangle network [1]. Recently, triangle networks along with other network scenarios have been analyzed from different perspectives [27][28][29]. However, to the best of the author's knowledge, there does not exist any criterion to detect nontrilocality in such a scenario.…”

Section: Motivationmentioning

confidence: 99%

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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“…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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Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniques

Cited by 26 publications

References 50 publications

Complex quantum networks: a topical review

Complex quantum networks: a topical review

Detecting Nontrilocal Correlations In Triangle Networks

Hidden Non n-locality In Linear Networks

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