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Physical Review A

Average correlation as a resource of quantum teleportation

You-neng Guo, Xiangjun Chen, Hu-Ping Peng, Qinglong Tian

Published Oct 6, 2025• 1 citation
Publisher

Abstract

Bell nonlocality and quantum steering are recognized as two important physical resources and offer quantum advantages in modern quantum information processing. Inspired by the asymmetric relations of teleportation to Bell nonlocality and quantum steering, in this paper we unify the maximal violation of Bell inequality and the maximal violation of the three-setting linear steering inequality by introducing the concept of average correlation and manage to establish the relation of average correlation to quantum teleportation. Particularly, we propose a necessary and sufficient condition for any two-qubit state with nonclassicality in terms of average correlation for teleportation. Our results suggest that average correlation is not only used to detect the nonclassicality of quantum states, but also can be useful as a potential resource for teleportation.

DOI
10.1103/lmdx-dk95

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Abstract Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation [ Phys. Rev. Res. 5 023063 (2023)], in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.
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Entanglement, quantum steering and Bell nonlocality can be used to describe the distinct quantum correlations of quantum systems. Because of their different characteristics and application fields, how to divide them quantitatively and accurately becomes particularly important. Based on the sufficient and necessary criterion for quantum steering of an arbitrary two-qubit T-state, we derive the inequality relations between quantum steering and entanglement as well as between quantum steering and Bell nonlocality for the T-state. Additionally, we have verified those relations experimentally.
Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direction by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e., lead to deterministic violation of Bell's inequality. Our result also extends the phenomenon of superactivation of quantum nonlocality, recently proven by C. Palazuelos [Phys. Rev. Lett. 109, 190401 (2012)], and suggests that the latter might in fact be more general than initially thought.
EPR steering is an important quantum resource in quantum information and computation. In this paper, its applications in quantum teleportation are investigated. First of all, the upper bound of the average teleportation fidelity based on the EPR steering is derived. When the receiver can only perform the identity or the Pauli rotation operations, the X-type states which violate the three-setting linear steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of the two-qubit reduced states for three-qubit pure states maintain the same ordering. The complementary relations between the steerable observables and the average teleportation fidelities for three-qubit pure states are also established.