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Physical Review A

Manipulating the quantum steering direction with sequential unsharp measurements

Zhao-Qi-Zhi Han, Hui-Chao Qu, Xuan Fan, Ya Xiao, Yongjian Gu

Published Oct 13, 2022• 13 citations
Publisher

Abstract

Quantum steering exhibits an inherent asymmetric property that differs from both quantum entanglement and Bell nonlocality, which leads to no-way, one-way, and two-way steering. Flexibly manipulating the direction of quantum steering without reducing the quantum steerability is very important for information processing. In this paper, implementing sequential unsharp measurements and the steering-radius criterion, we show how to manipulate that steering direction among multiple Alices and Bobs. We demonstrate that the change in steering direction depends on the number of measurement settings and the sharpness of measurements. For a given two-qubit asymmetric state, we obtain 13 kinds of steering regions with different steering directions in the case of one Alice and three Bobs and obtain 11 kinds in the case with two Alices and two Bobs. For the case with one Alice and three Bobs, we further find a volume bound to visualize quantum steering. Our manipulation scheme is experimentally easy to achieve and rather assigns the steerability to more observers without reducing it, which offers a direct reference for the practical application of quantum steering.

DOI
10.1103/physreva.106.042416

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Quantum steering exhibits an inherent asymmetric property that differs from both quantum entanglement and Bell nonlocality, which leads to no-way, one-way, and two-way steering. Flexibly manipulating the direction of quantum steering without reducing the quantum steerability is very important for information processing. In this paper, implementing sequential unsharp measurements and the steering-radius criterion, we show how to manipulate that steering direction among multiple Alices and Bobs. We demonstrate that the change in steering direction depends on the number of measurement settings and the sharpness of measurements. For a given two-qubit asymmetric state, we obtain 13 kinds of steering regions with different steering directions in the case of one Alice and three Bobs and obtain 11 kinds in the case with two Alices and two Bobs. For the case with one Alice and three Bobs, we further find a volume bound to visualize quantum steering. Our manipulation scheme is experimentally easy to achieve and rather assigns the steerability to more observers without reducing it, which offers a direct reference for the practical application of quantum steering.
Abstract Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings N increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed N, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied.
Noise-adding methods have been widely used to manipulate the direction of quantum steering, but all related experimental schemes only worked under the assumption that Gaussian measurements were performed and ideal target states were accurately prepared. Here, we prove, and then experimentally observe, that a class of two-qubit states can be flexibly changed among two-way steerable, one-way steerable and no-way steerable, by adding either phase damping noise or depolarization noise. The steering direction is determined by measuring steering radius and critical radius, each of which represents a necessary and sufficient steering criterion valid for general projective measurements and actually prepared states. Our work provides a more efficient and rigorous way to manipulate the direction of quantum steering, and can also be employed to manipulate other types of quantum correlations.
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. A natural question is then whether there exist entangled states which are one-way steerable, that is, Alice can steer Bob's state, but it is impossible for Bob to steer the state of Alice. So far, such a phenomenon has been demonstrated for continuous variable systems, but with a strong restriction on allowed measurements, namely, considering only Gaussian measurements. Here we present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.
Einstein-Podolsky-Rosen (EPR) steering exhibits an inherent asymmetric feature that differs from both entanglement and Bell nonlocality, which leads to one-way EPR steering. Although this one-way EPR steering phenomenon has been experimentally observed, the schemes to manipulate the direction of EPR steering have not been investigated thoroughly. In this paper, we propose and experimentally demonstrate three schemes to manipulate the direction of EPR steering, either by varying the noise on one party of a two-mode squeezed state (TMSS) or transmitting the TMSS in a noisy channel. The dependence of the direction of EPR steering on the noise and transmission efficiency in the quantum channel is analyzed. The experimental results show that the direction of EPR steering of the TMSS can be changed in the presented schemes. Our work is helpful in understanding the fundamental asymmetry of quantum nonlocality and has potential applications in future asymmetric quantum information processing.
Einstein-Podolsky-Rosen (EPR) steering describes the ability of one party to remotely affect another's state through local measurements. One of the most distinguishable properties of EPR steering is its asymmetric aspect. Steering can work in one direction but fail in the opposite direction. This type of one-way steering, which is different from the symmetry concepts of entanglement and Bell nonlocality, has garnered much interest. However, an experimental demonstration of genuine one-way EPR steering in the simplest scenario, i.e., one that employs two-qubit systems, is still lacking. In this Letter, we experimentally demonstrate one-way EPR steering with multimeasurement settings for a class of two-qubit states, which are still one-way steerable even with infinite settings. The steerability is quantified by the steering radius, which represents a necessary and sufficient steering criterion. The demonstrated one-way steering in the simplest bipartite quantum system is of fundamental interest and may provide potential applications in one-way quantum information tasks.