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arXiv:2209.07110 · Entropy

Detecting Tripartite Steering via Quantum Entanglement

Zhihua Chen, Shao-Ming Fei

Published Sep 14, 2022• 4 citations
arXivHTMLPDF

Abstract

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.

DOI
10.3390/e24091297

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International Conference on Systems and Informatics (ICSAI)•Nov 1, 2016•0 citations
Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.
Quantum inseparabilities can be classified into three inequivalent forms: entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Bell-nonlocal states form a strict subset of EPR steerable states which also form a strict subset of entangled states. Recently, EPR steerable states have been shown to be fundamental resources for one-sided device-independent quantum information processing tasks and, hence, identification of EPR steerable states becomes important from foundational as well as informational theoretic perspectives. In the present paper, we propose a criterion to detect whether a given two-qubit state is EPR steerable. From an arbitrary given two-qubit state, another two-qubit state is constructed in such a way that the given state is EPR steerable if the new constructed state is entangled. Hence, EPR steerability of an arbitrary two-qubit state can be detected by detecting entanglement of the newly constructed state. Apart from providing a distinctive way to detect EPR steering without using any steering inequality, the present paper also provides an alternative way to avoid locality loopholes in EPR steering tests and to reduce the ``complexity cost'' present in experimentally detecting EPR steering. We also generalize our criteria to detect EPR steering of higher dimensional quantum states. Finally, we illustrate our result by using our proposed technique to detect EPR steerability of various families of mixed states.
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.
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.
Quantum steering is considered one of the most well-known nonlocal phenomena in quantum mechanics. Unlike entanglement and Bell nonlocality, the asymmetry of quantum steering makes it vital for one-sided device-independent quantum information processing. Although there has been much progress on steering detection for bipartite systems, the criterion for Einstein-Podolsky-Rosen steering in tripartite systems remains challenging and inadequate. In this paper we first derive a promising steering criterion for any three-qubit states via correlation matrix. Furthermore, we propose the monogamy relation between the tripartite steering of system and the bipartite steering of subsystems based on the derived criterion. Finally, as illustrations, we demonstrate the performance of the steering criterion and the monogamy relation by means of several representative examples. We believe that the results and methods presented in this work could be beneficial to capture genuine multipartite steering in the near future.
The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning the EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-qubit state, we observe the EPR steering by detecting the entanglement of these new states. The results show that the entanglement of the newly constructed states can be regarded as an unusual kind of steering witness for these states. Compared to the results of Xiao et al. [Phys. Rev. Lett. 118, 140404 (2017)], we find that the ability to detect the EPR steering in our scenario is stronger than that of two-setting projective measurements, which can observe more steerable states. Hence, our demonstrations can deepen the understanding of the connection between the EPR steering and entanglement.
EPR steering is a form of bipartite quantum correlation that is intermediate between entanglement and Bell nonlocality. It is detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Furthermore, there is a sufficient criterion for guaranteeing that a two-qubit state is unsteerable. But there are some two qubit states that can not determine the steerability of the steering inequality and the sufficient criteria. Here we introduce a way of quantifying this phenomenon and use it to study the steerability of two qubit states. This article recommend a platonic solid measurement schemes. And then discuss the problem, namely expanding the scope of steerable, which guarantees that the state is steerable.