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arXiv:2208.06861 · Physical Review A

Persistency of non- n -local correlations in noisy linear networks

Kaushiki Mukherjee, Indranil Chakrabarty, Ganesh Mylavarapu

Published Mar 3, 2023• 16 citations
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Abstract

Linear $n$-local networks are compatible with quantum-repeater-based entanglement distribution protocols. Different sources of imperfections such as error in entanglement generation, communication over noisy quantum channels, and imperfections in measurements result in decay of quantumness across such networks. From practical perspectives it becomes imperative to analyze the nonclassicality of quantum network correlations in the presence of different types of noise. The present discussion provides a formal characterization of non-$n$-local features of quantum correlations in a noisy network scenario. In this context, persistency of non-$n$-locality has been introduced. Such a notion helps in analyzing decay of non-$n$-local features of network correlations with increasing length of the linear network in the presence of one or more causes of imperfections.

DOI
10.1103/physreva.107.032404

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Linear nnn-local networks are compatible with quantum-repeater-based entanglement distribution protocols. Different sources of imperfections such as error in entanglement generation, communication over noisy quantum channels, and imperfections in measurements result in decay of quantumness across such networks. From practical perspectives it becomes imperative to analyze the nonclassicality of quantum network correlations in the presence of different types of noise. The present discussion provides a formal characterization of non-nnn-local features of quantum correlations in a noisy network scenario. In this context, persistency of non-nnn-locality has been introduced. Such a notion helps in analyzing decay of non-nnn-local features of network correlations with increasing length of the linear network in the presence of one or more causes of imperfections.
Abstract The topic of network quantum nonlocal correlations arises from the large-scale quantum communications. It has been demonstrated that non-m-local correlations (m is the number of sources) in some special kinds of networks will decay under the influence of noises from imperfect devices as these networks extend, including linear and star networks. Furthermore, we observe that under the same noisy level, persistency of non-multi-local correlations in aforementioned different kinds of networks appears obvious discrepancy. Therefore, it becomes a natural and challenging task to check the persistency of non-multi-locality in more complex acyclic network, since star and linear networks can be regarded as acyclic networks. It is worth noting that an acyclic network is one indeterminate forked tree-shaped networks. So the study is focused on the tree-shaped network. We first devote to discussing the determinate forked case. We obtain inequality persistency criteria of determinate k-forked tree-shaped network non-(s n (k))-local correlations (s n (k) is the number of total sources). We show that the larger the fork number k is larger, the better the non-multi-locality of this network persists. In the indeterminate forked case, the inequality persistency criteria are also established. We observe that the larger the number of parties in the last layer of an acyclic network, the better the non-multi-locality of this network is persisted. This theoretical research may guide us how to build quantum networks with the stronger correlation in practical communications.
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-nnn-locality in two distinct network topologies (linear and star). We have studied the extremal violations of nnn-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-nnn-locality in a linear network. However, the same is not true for star nnn-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-nnn-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the nnn-local inequalities is also provided. Interestingly, detection of non-nnn-locality is ensured in the network if product of concurrence of all the sources involved exceeds 12.\frac{1}{2}.21​.
Imperfections from devices can result in the decay or even vanish of non-n-local correlations as the number of parties n increases in the polygon and linear quantum networks ([Phys. Rev. A 106, 042206 (2022)] and [Phys. Rev. A 107, 032404 (2023)]). Even so this phenomenon is also for the special kind of noises, including consistency noises of a sequence of devices, which means the sequence of devices have the same probability fails to detect. However, in the paper, we discover that star network quantum non-n-local correlations can resist better consistency noises than these in polygon and linear networks. We first calculate the noisy expected value o f star network non-n-locality and analyze the persistency conditions theoretically. When assume that congener devices have the consistency noise, the persistency number of sources n has been rid of such noises, and approximates to the infinity. Polygon and linear network non-n-local correlations can not meet the requirements. Furthermore, we explore the change pattern of the maximal number of sources nmax such that non-nmax-local correlation can be demonstrated in the star network under the influence of partially consistent noises, which is more general than consistent ones.
It was showed in [Phys. Rev. Lett. 125 090401 (2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob’s half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.
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 nnn-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.
Quantum networks allow for novel forms of quantum nonlocality. By exploiting the combination of entangled states and entangled measurements, strong nonlocal correlations can be generated across the entire network. So far, all proofs of this effect are essentially restricted to the idealized case of pure entangled states and projective local measurements. Here we present noise-robust proofs of network quantum nonlocality, for a class of quantum distributions on the triangle network that are based on entangled states and entangled measurements. The key ingredient is a result of approximate rigidity for local distributions that satisfy the so-called “parity token counting'' property with high probability. Our methods can be applied to any type of noise. As illustrative examples, we consider quantum distributions obtained with imperfect sources and obtain a noise robustness up to ∼80% for dephasing noise and up to ∼0.5% for white noise. Additionally, we prove that all distributions in the vicinity of some ideal quantum distribution are nonlocal, with a bound on the total-variation distance ∼0.25% . Our work opens interesting perspectives towards the practical implementation of quantum network nonlocality.