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arXiv:2312.05769 · Results in Physics

Detection of network and genuine network quantum steering

Zhihua Chen, Kai Wu, Shao-Ming Fei

Published Dec 5, 2023• 7 citations
arXivHTMLPDF

Abstract

The quantum network correlations play significant roles in long distance quantum communication, quantum cryptography and distributed quantum computing. Generally it is very difficult to characterize the multipartite quantum network correlations such as nonlocality, entanglement and steering. In this paper, we propose the network and the genuine network quantum steering models from the aspect of probabilities in the star network configurations. Linear and nonlinear inequalities are derived to detect the network and genuine network quantum steering when the central party performs one fixed measurement. We show that our criteria can detect more quantum network steering than that from the violation of the $n$-locality quantum networks. Moreover, it is shown that biseparable assemblages can demonstrate genuine network steering in the star network configurations.

DOI
10.1016/j.rinp.2023.107244

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The quantum network correlations play significant roles in long distance quantum communication, quantum cryptography and distributed quantum computing. Generally it is very difficult to characterize the multipartite quantum network correlations such as nonlocality, entanglement and steering. In this paper, we propose the network and the genuine network quantum steering models from the aspect of probabilities in the star network configurations. Linear and nonlinear inequalities are derived to detect the network and genuine network quantum steering when the central party performs one fixed measurement. We show that our criteria can detect more quantum network steering than that from the violation of the nnn-locality quantum networks. Moreover, it is shown that biseparable assemblages can demonstrate genuine network steering in the star network configurations.
In this work, we will consider the star network scenario where the central party is trusted while all the edge parties (with a number of nnn) are untrusted. Network steering is defined with an nnn local hidden state model which can be viewed as a special kind of nnn local hidden variable model. Two different types of sufficient criteria, nonlinear steering inequality and linear steering inequality will be constructed to verify the quantum steering in a star network. Based on the linear steering inequality, how to detect the network steering with a fixed measurement will be discussed.
Abstract In this work, we will consider the star network scenario where the central party is trusted while all the edge parties (with a number of n ) are untrusted. Network steering is defined with an n local hidden state model which can be viewed as a special kind of n local hidden variable model. Two different types of sufficient criteria, nonlinear steering inequality and linear steering inequality will be constructed to verify the quantum steering in a star network. Based on the linear steering inequality, how to detect the network steering with a fixed measurement will be discussed.
Network quantum steering plays a pivotal role in quantum information science, enabling robust certification of quantum correlations in scenarios with asymmetric trust assumptions among network parties. The intricate nature of quantum networks, however, poses significant challenges for the detection and quantification of steering. In this work, we develop a neural network-based method for measuring network quantum steerability, which can be generalized to arbitrary quantum networks and naturally applied to standard steering scenarios. Our method provides an effective framework for steerability analysis, demonstrating remarkable accuracy and efficiency in standard bipartite and multipartite steering scenarios. Numerical simulations involving isotropic states and noisy Greenberger-Horne-Zeilinger states yield results that are consistent with established findings in these respective scenarios. Furthermore, we demonstrate its utility in the bilocal network steering scenario, where an untrusted central party shares two-qubit isotropic states of different visibilities, $\ensuremath{\nu}$ and $\ensuremath{\omega}$, with trusted end-point parties and performs a single Bell state measurement. Through explicit construction of a network local hidden state model derived from numerical results and incorporation of the entanglement properties of network assemblages, we analytically demonstrate that the network steering thresholds are determined by the curve $\ensuremath{\nu}\ensuremath{\omega}=1/3$ under the corresponding configuration.
Quantum network correlations are crucial for long-distance quantum communication, quantum cryptography, and distributed quantum computing. Detecting network steering is particularly challenging in complex network structures. We have studied the steering inequality criteria for a 2-forked 3-layer tree-shaped network. Assuming the first and third layers are trusted and the second layer is untrusted, we derived a steering inequality criterion using the correlation matrix between trusted and untrusted observables. In particular, we apply the steering criterion to three classes of measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We further illustrate the effectiveness of our method through an example.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
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​.