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Physical Review A

Einstein-Podolsky-Rosen steering and monogamy relations in controllable dynamical Casimir arrays

Mengxin Zhang, Yumei Long, Shiqing Zhao, Xue Zhang

Published Apr 27, 2022• 5 citations
Publisher

Abstract

We achieve the controllable multipartite Einstein-Podolsky-Rosen (EPR) steering and its monogamy relations by means of the dynamical Casimir effect in the frame of superconducting quantum network. We employ the external driving flux of the superconducting quantum interference device as a switch. It is interesting that the system exhibits different types of the EPR steering and monogamy relations by tuning parameters. In the system, the one-way or two-way EPR steerings for different parties have been realized, and the direction of the one-way EPR steering is reversed by tuning coupling parameters. Remarkably, we can also obtain the EPR steering orderly sudden death for different modes. In addition, the system not only shows the type-I and type-II monogamy relations, but also converts steering parties to get monogamy relations' swapping and cycling. Finally, we discuss the influence of temperature. In the system, the higher the temperature is, the earlier sudden death for the EPR steering is. These results are important for quantum information and lay a foundation for us to better understand the important role of the multipartite EPR steering in secure quantum communication.

DOI
10.1103/physreva.105.042435

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We achieve the controllable multipartite Einstein-Podolsky-Rosen (EPR) steering and its monogamy relations by means of the dynamical Casimir effect in the frame of superconducting quantum network. We employ the external driving flux of the superconducting quantum interference device as a switch. It is interesting that the system exhibits different types of the EPR steering and monogamy relations by tuning parameters. In the system, the one-way or two-way EPR steerings for different parties have been realized, and the direction of the one-way EPR steering is reversed by tuning coupling parameters. Remarkably, we can also obtain the EPR steering orderly sudden death for different modes. In addition, the system not only shows the type-I and type-II monogamy relations, but also converts steering parties to get monogamy relations' swapping and cycling. Finally, we discuss the influence of temperature. In the system, the higher the temperature is, the earlier sudden death for the EPR steering is. These results are important for quantum information and lay a foundation for us to better understand the important role of the multipartite EPR steering in secure quantum communication.
Abstract We design dynamical Casimir arrays (DCA) consisting of giant atoms and coupled resonator waveguides (CRWs) to investigate the Einstein–Podolsky–Rosen (EPR) steering at finite temperatures. Our designed system exhibits an asymmetry in its structure, which is caused by the differences in the sizes and the coupling positions of the giant atoms. The system achieves different types of EPR steering and the reversal of one-way EPR steering by modulating parameters. Furthermore, the symmetry and asymmetry of the system structure, in their responses to parameter modulation, both reveal the asymmetry of EPR steering. In this process, we discover that with the increase in temperature, different types of steering can be transferred from Casimir photons to giant atoms. We also achieve the monogamy of the multipartite system. These results provide important assistance for secure quantum communication, and further intuitively validating the asymmetry of EPR steering from multiple perspectives.
Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.
Abstract Einstein–Podolsky–Rosen (EPR) steering is different from quantum entanglement because of its unique asymmetry. Multipartite asymmetric EPR steering can break through one-to-one monogamy steering and achieve one to many one-way steering. That is to say, the state of one part can steer the other rest parts simultaneously, while the other parts cannot steer this part. Here, a scheme is proposed to generate one to many one-way steering by optical parametric amplification cascaded with a sum-frequency generation process. One to many non-monogamy EPR steering, such as one to two and one to three one-way steering are demonstrated based on the criterion for asymmetric EPR steering. It is also find that different kinds of asymmetric EPR steering can be obtained by choosing different nonlinear parameters. This non-monogamous one to many quantum control has potential application in constructing quantum networks and realizing one-way quantum computing.
Multipartite Einstein-Podolsky-Rosen (EPR) steering has been recognized as an essential resource for secure quantum communication tasks composed of several spatially separated parties who cannot be fully trusted. Nevertheless, this resource cannot be distributed arbitrarily over many parties; for instance, two independent players cannot simultaneously steer the third party by two-setting measurements. This feature is referred to as monogamy of steering, which ensures the security of quantum cryptographic protocols and is thus a very desired property to investigate for multipartite steering. Here, we propose symmetric and asymmetric structures of cascaded four-wave mixing of rubidium atoms to generate versatile quadripartite EPR steering and investigate four distinct types of monogamy relations of Gaussian steering. We find that the distribution constraint described by one of the monogamy relations can be lifted only for the quadripartite steering created by the symmetric setup. This result paves the way for a better understanding of the distribution rules of multipartite EPR steering and its potential applications for secure quantum communication.
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.
Monogamy inequalities for the way bipartite Einstein-Podolsky-Rosen (EPR) steering can be distributed among NNN systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalize to mmm settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to mmm, and takes a form similar to the Coffman-Kundu-Wootters relation for entanglement. The results enable characterization of the tripartite steering for CV Gaussian systems and qubit Greenberger-Horne-Zeilinger and WWW states.