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arXiv:2201.08028 · Physical Review A

One-way Einstein-Podolsky-Rosen steering beyond qubits

Qiang Zeng

Published Sep 2, 2022• 13 citations
arXivHTMLPDF

Abstract

Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric under the exchange of parties have been found to manifest steering only in a specific direction, thus called one-way steering. Existing works focused on one-way steering in systems of qubits. Here we propose a family of two-party states that are one-way steerable in systems of $d$ dimensions. In particular, we validate the one-way steerability of the states for $d=3$, and demonstrate how one-way steering parameter space manifests in a two-qutrit system. A general numerical approach for characterizing higher-dimensional one-way steering is provided. Moreover, we develop a method to characterize one-way steering with the experimental loss taken into account, with which the trade-off relation between losses and measurement settings in a steering test in higher-dimensional system is investigated. Our loss-counted model works for finite-dimensional systems with finite measurement settings.

DOI
10.1103/physreva.106.032202

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Quantum steering has been exploited as an important resource in modern quantum information processing. Owing to its directional nature, some quantum states that are asymmetric under the exchange of parties have been found to manifest steering only in a specific direction, thus called one-way steering. Existing works focused on one-way steering in systems of qubits. Here we propose a family of two-party states that are one-way steerable in systems of ddd dimensions. In particular, we validate the one-way steerability of the states for d=3d=3d=3, and demonstrate how one-way steering parameter space manifests in a two-qutrit system. A general numerical approach for characterizing higher-dimensional one-way steering is provided. Moreover, we develop a method to characterize one-way steering with the experimental loss taken into account, with which the trade-off relation between losses and measurement settings in a steering test in higher-dimensional system is investigated. Our loss-counted model works for finite-dimensional systems with finite measurement settings.
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.
Abstract Einstein–Podolsky–Rosen steering refers to the quantum phenomenon whereby the state of a system held by one party can be ‘steered’ into different states at the will of another, distant, party by performing different local measurements. Although steering has been demonstrated in a number of experiments involving qubits, the question of which two-qubit states are steerable remains an open theoretical problem. Here, we derive a necessary condition for any two-qubit state to be steerable when the steering party suffers from a given probability of qubit loss. Our main result finds application in one-way steering demonstrations that rely upon loss. Specifically, we apply it to a recent experiment on one-way steering with projective measurements and POVMs, reported by Wollmann et al (2016 Phys. Rev. Lett. 116 160403).
Quantum steering is a recently defined form of quantum correlation which lies at the heart of quantum mechanics. In contrast to other types of quantum correlations, quantum steering is inherently asymmetric, which implies that it could manifest in one direction but not in the opposite direction. This rather peculiar phenomenon, known as one-way steering, has been demonstrated in several experiments, but subtlety remains. In fact, all experiments were shown to be ambiguous until a very recent conclusive one, which, however, made crucial use of a high-dimensional embedding to get around assumptions. This leaves the question open of whether the one-way steering phenomenon can be reliably demonstrated in the genuine two-qubit system. Here, we report such an experimental demonstration of one-way steering for a family of two-qubit states. Our experimental setup and results thus resolve the subtlety caused by fidelity assumption in previous experiments without the need for higher dimensional embedding. Moreover, our work provides a universal method to characterize one-way steering phenomenon for generic two-qubit states.
Occupying a position between entanglement and Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering has attracted increasing attention in recent years. Many criteria have been proposed and experimentally implemented to characterize EPR-steering. Nevertheless, only a few results are available to quantify steerability using analytical results. In this work, we propose a method for quantifying the steerability in two-qubit quantum states in the two-setting EPR-steering scenario, using the connection between joint measurability and steerability. We derive an analytical formula for the steerability of a class of X-states. The sufficient and necessary conditions for two-setting EPR-steering are presented. Based on these results, a class of asymmetric states, namely, one-way steerable states, are obtained.
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, a distinctive quantum correlation, reveals a unique and inherent asymmetry. This research delves into the multifaceted asymmetry of EPR steering within high-dimensional quantum systems, exploring both theoretical frameworks and experimental validations. We introduce the concept of genuine high-dimensional one-way steering, wherein a high Schmidt number of bipartite quantum states is demonstrable in one steering direction but not reciprocally. Additionally, we explore two criteria to certify the lower and upper bounds of the Schmidt number within a one-sided device-independent context. These criteria serve as tools for identifying potential asymmetric dimensionality of EPR steering in both directions. By preparing two-qutrit mixed states with high fidelity, we experimentally observe asymmetric structures of EPR steering in the C^{3}⊗C^{3} Hilbert space. Our Letter offers new perspectives to understand the asymmetric EPR steering beyond qubits and has potential applications in asymmetric high-dimensional quantum information tasks.