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High-dimensional measurement-device-independent quantum steering and its application in randomness generation

Yu Guo, Shuming Cheng, Xiao‐Min Hu, Bi‐Heng Liu, En-Ming Huang, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo, Eric G. Cavalcanti

Published Dec 30, 2018• 0 citations
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Abstract

In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of non-orthogonal quantum states. In this work, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract $1.106\pm0.023$ bits of private randomness from our observed data, which surpasses the one-bit limit for qubit systems. Our results advance research on quantum information processing tasks beyond qubits.

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In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of non-orthogonal quantum states. In this work, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.0231.106\pm0.0231.106±0.023 bits of private randomness from our observed data, which surpasses the one-bit limit for qubit systems. Our results advance research on quantum information processing tasks beyond qubits.
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.023 bits of private randomness per every photon pair from our observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems. Our results advance research on quantum information processing tasks beyond qubits.
Entanglement lies at the heart of quantum mechanics, and has been identified as an essential resource for diverse applications in quantum information. If entanglement could be verified without any trust in the devices of observers, i.e., in a device-independent (DI) way, then high security could be guaranteed for various quantum information processing tasks. In this work, we propose and experimentally demonstrate a DI protocol to certify the presence of entanglement based on Einstein–Podolsky–Rosen (EPR) steering. We first establish the DI verification framework by taking advantage of a measurement-device-independent technique and self-testing, which is able to verify all bipartite EPR-steerable states. In the scenario of three-measurement settings per party, the protocol is robust in tolerance of inefficient measurements and imperfect self-testing. Moreover, a four-photon experiment is implemented for verification beyond Bell nonlocal states. Our work enables further insight into quantum physics and could facilitate realistic implementation of secure quantum information processing tasks.
Abstract If the presence of entanglement could be certified in a device-independent (DI) way, it is likely to provide various quantum information processing tasks with unconditional security. Recently, it was shown that a DI protocol, combining measurement-device-independent techniques with self-testing, is able to verify all entangled states, however, it imposes demanding requirements on its experimental implementation. In this work, we propose a much less-demanding protocol based on Einstein-Podolsky-Rosen (EPR) steering to certify entanglement. We establish a complete framework for DI verification of EPR steering in which all steerable states could be verified. We then analyze its robustness towards noise and imperfections of self-testing by considering the measurement scenario with three settings at each side. Finally, a four-photon experiment is implemented to demonstrate that even Bell local states can be device-independently verified. Our work may pave the way for realistic applications of secure quantum information tasks.
Abstract Einstein–Podolsky–Rosen (EPR) steering allows two parties to verify their entanglement, even if one party’s measurements are untrusted. This concept has not only provided new insights into the nature of non-local spatial correlations in quantum mechanics, but also serves as a resource for one-sided device-independent quantum information tasks. Here, we investigate how EPR steering behaves when one-half of a maximally entangled pair of qudits (multidimensional quantum systems) is cloned by a universal cloning machine. We find that EPR steering, as verified by a criterion based on the mutual information between qudits, can only be found in one of the copy subsystems but not both. We prove that this is also true for the single-system analogue of EPR steering. We find that this restriction, which we term ‘no-cloning of quantum steering’, elucidates the physical reason why steering can be used to secure sources and channels against cloning-based attacks when implementing quantum communication and quantum computation protocols.
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.
We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.