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Physical Review A

Quantum steering as resource of quantum teleportation

Yi Fan, Chuan-Lei Jia, Liang Qiu

Published Jul 25, 2022• 19 citations
Publisher

Abstract

Quantum steering, which lies between Bell nonlocality and entanglement, is a characteristic quantum correlation. Its application in quantum information tasks is worth pursuing. In this paper, we investigate the application of quantum steering as resource of quantum teleportation. It is found that two-qubit states violating the three-setting linear steering inequality are always useful for teleportation. Some steerable states which obey the Bell--Clauser-Horne-Shimony-Holt (CHSH) inequality could be used for teleportation. Two-qubit states that are optimal for quantum teleportation for a fixed amount of steering are present. The optimal states achieve the maximal average fidelity and also exhibit zero fidelity deviation.

DOI
10.1103/physreva.106.012433

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Journal of Physics A Mathematical and Theoretical•Apr 5, 2023•3 citations
Quantum steering, which lies between Bell nonlocality and entanglement, is a characteristic quantum correlation. Its application in quantum information tasks is worth pursuing. In this paper, we investigate the application of quantum steering as resource of quantum teleportation. It is found that two-qubit states violating the three-setting linear steering inequality are always useful for teleportation. Some steerable states which obey the Bell--Clauser-Horne-Shimony-Holt (CHSH) inequality could be used for teleportation. Two-qubit states that are optimal for quantum teleportation for a fixed amount of steering are present. The optimal states achieve the maximal average fidelity and also exhibit zero fidelity deviation.
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.
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.
Quantum teleportation with a two-qubit state can be suitably characterized in terms of maximal fidelity and fidelity deviation---the former is the maximal value of the average fidelity achievable within the standard protocol and local unitary operations and the latter is the standard deviation of fidelity over all input states. In this paper, we consider the problem of characterizing two-qubit states that are optimal for quantum teleportation for a given value of some state property. The optimal states are defined as those states that, for a given value of the state property under consideration, achieve the largest maximal fidelity and also exhibit zero fidelity deviation. We provide a complete characterization of optimal states for a given linear entropy, maximum mean value of the Bell--Clauser-Horne-Shimony-Holt (CHSH) observable, and concurrence, respectively. We find that for a given linear entropy or Bell-CHSH violation the largest maximal fidelity states are optimal, but for a given concurrence the optimal states form a strict subset of the largest maximal fidelity states.
Steerability is a characteristic of quantum correlations lying between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring the security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three-qubit state can violate the three-setting CJWR linear steering inequality, contrary to the two-setting linear steering inequality. This result explains that quantum steering correlations have limited shareability properties apart from the conventional 'nonshareable' monogamy constraint. In contrast to the two-measurement-setting scenario, the three-setting scenario turns out to be more useful for developing a deeper understanding of the shareability of tripartite steering correlations. Apart from the distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states, and genuine tripartite entanglement are presented here. The results enable the detection of different kinds of tripartite entanglement.
We derive an inequality that is necessary and sufficient to show Einstein-Podolsky-Rosen (EPR) steering in a scenario employing only correlations between two arbitrary dichotomic measurements on each party. Thus the inequality is a complete steering analogy of the Clauser-Horne-Shimony-Holt (CHSH) inequality, a generalization of the result of Cavalcanti et al. [E. G. Cavalcanti, C. J. Foster, M. Fuwa, and H. M. Wiseman, JOSA B 32, A74 (2015)]. We show that violation of the inequality only requires measuring over equivalence classes of mutually unbiased measurements on the trusted party and that in fact assuming a general two-qubit system arbitrary pairs of distinct projective measurements at the trusted party are equally useful. Via this it is found that for a given state the maximum violation of our EPR-steering inequality is equal to that for the CHSH inequality, so all states that are EPR steerable with CHSH-type correlations are also Bell nonlocal.
Abstract Einstein–Podolsky–Rosen (EPR) steering is an important quantum resource in quantum information and computation. The relationships between EPR steering and the fidelity of quantum teleportation for two- and three-qubit states are investigated in this paper. For two-qubit states, 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 two-qubit X-type states which violate the three-setting measurements steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of two-qubit reduced states for three-qubit pure states maintain the same ordering. The complementary relations between the steering observables and the average teleportation fidelities for three-qubit pure states are also established.