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Journal of the Optical Society of America B

Asymmetric quantum network based on multipartite Einstein–Podolsky–Rosen steering

Meng Wang, Yu Xiang, Qiongyi He, Qihuang Gong

Published Mar 9, 2015• 8 citations
Publisher

Abstract

In this work, we propose an asymmetric multi-user access optical network with hierarchical structure in terms of steering ability. The N-partite system is generated by mixing two squeezed lights and N−2 vacuum modes at N−1 beam splitters. The asymmetry of this system can be constructed by choosing proper reflectivities of beam splitters and introducing asymmetric loss to channels of the network, such that the steering ability is distributed asymmetrically among users. By proper construction, one superior in the network possesses higher steering ability than any one of the remaining N−1 subordinates. We show how to accomplish the directional quantum steering between them, i.e., the superior can apparently steer any subordinate’s state, but it cannot always happen in the opposite direction. In addition, we quantify the thresholds of loss tolerance that will prevent the extraction of information of the superior by M(1≤M≤N−1) subordinates’ local measurements. An important feature of such a network is that the superior can send a secret message to certain subordinates without trustworthy assumptions about them and their apparatus. Our findings have applications in one-sided device-independent quantum communication protocol with multi-users.

DOI
10.1364/josab.32.000a20

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In this work, we propose an asymmetric multi-user access optical network with hierarchical structure in terms of steering ability. The N-partite system is generated by mixing two squeezed lights and N−2 vacuum modes at N−1 beam splitters. The asymmetry of this system can be constructed by choosing proper reflectivities of beam splitters and introducing asymmetric loss to channels of the network, such that the steering ability is distributed asymmetrically among users. By proper construction, one superior in the network possesses higher steering ability than any one of the remaining N−1 subordinates. We show how to accomplish the directional quantum steering between them, i.e., the superior can apparently steer any subordinate’s state, but it cannot always happen in the opposite direction. In addition, we quantify the thresholds of loss tolerance that will prevent the extraction of information of the superior by M(1≤M≤N−1) subordinates’ local measurements. An important feature of such a network is that the superior can send a secret message to certain subordinates without trustworthy assumptions about them and their apparatus. Our findings have applications in one-sided device-independent quantum communication protocol with multi-users.
The multipartite entangled state has drawn broad attention for both foundations of quantum mechanics and applications in quantum information processing. Here, we study the spatially separated NNN-partite continuous-variable Greenberger-Horne-Zeilinger--like states, which can be produced by a linear optical network with squeezed light and $N\ensuremath{-}1$ beamsplitters. We investigate the properties of multipartite Einstein-Podolsky-Rosen steering possessed by those states, and find that the steering of a given quantum mode is allowed when not less than half of the modes within the states take part in the steering group. This is certified by the detection of the correlation between position and momentum quadratures of the steered mode and a combination of quadratures of other modes inside the steering group. The steering is evidenced by the high correlation where the steering group can infer the quadratures of the steered mode to high precision, i.e., below the quantum limit for the position and momentum quadratures of the steered quantum mode. We also examine the influence of inefficiency on the multipartite steering, and derive the threshold of the loss tolerance. Furthermore, we discuss the collective NNN-partite steering induced by the asymmetric loss on beams, which exists when a given quantum mode can only be steered by all the remaining $N\ensuremath{-}1$ modes collaboratively. The present multipartite steering correlation may have potential applications in certain quantum information tasks where the issue of trust is important, such as one-sided device-independent quantum secret sharing.
The distribution of quantum correlations among remote users is a key procedure underlying many quantum information technologies. Einstein-Podolsky-Rosen steering, which is one kind of such a correlation stronger than entanglement, has been identified as a resource for secure quantum networks. We show that this resource can be established between two and even more distant parties by transmission of a system being separable from all the parties. For two-user scenarios, we design a protocol allowing one to distribute one-way Gaussian steering which can be used subsequently for one-sided device-independent (1sDI) quantum key distribution. Further, we extend the protocol to three-user scenarios to distribute richer steerability properties including one-to-multimode steering and collective steering which can be used for 1sDI quantum secret sharing. All the proposed protocols can be implemented with squeezed states, beam splitters, and displacements, and thus they can be readily realized experimentally. Our findings reveal that not only entanglement but even steering can be distributed via communication of a separable system. Viewed from a different perspective, the present protocols also demonstrate that one can switch multipartite states between different steerability classes by operations on parts of the states.
Asymmetric Einstein–Podolsky–Rosen (EPR) steering means the ability of one party to nonlocally “steer” the state in the other side through local measurements. The asymmetric property of EPR steering provides adequate security in one-sided device-independent secure quantum communication protocols. In this paper, we theoretically investigate the asymmetric EPR steering schemes between two subsystems of multipartite entangled states by an asymmetric modulation method. Two schemes, including tripartite entangled state to bipartite steering and quadripartite entangled state to tripartite steering, are investigated. By reconstructing the covariance matrix of continuous variable multipartite Gaussian states, we quantify the steerability of manipulating two different subsystems and demonstrate the EPR steering parameter versus various types of states’ parameters. Our work provides a reference for asymmetric quantum information processing and enriches resources for secure quantum networks.
We present a comprehensive phase diagram of quantum correlations in a three-mode Gaussian state generated by a tritter, driven by a two-mode squeezed vacuum and a coherent state. The coherent amplitude does not affect the correlation structure, which is solely governed by the initial squeezing. By systematically analyzing five physically relevant asymmetric loss configurations, we map out the exact resilience thresholds for entanglement and Einstein-Podolsky-Rosen (EPR) steering under all bipartite partitions. We reveal that EPR steering exhibits a pronounced directional asymmetry under loss, and its survival can be maintained over a much wider range of loss by strategically protecting a single channel. This tunable fragility provides practical guidance for one-sided device-independent quantum protocols in noisy asymmetric networks. We further confirm the limitations of Rényi-2 entropy in the quantification of entanglement and steering. Our results transform the abstract correlation hierarchy into a calculable, experimentally relevant guide for engineering robust quantum resources.
As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.
Collective multipartite Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation shared among nnn parties, where the EPR paradox of one party can be realized only by performing local measurements on all the remaining $n\ensuremath{-}1$ parties. Here, we propose an efficient method to produce collective multipartite EPR steering via symmetrically and asymmetrically cascading parametric amplification processes, i.e., four-wave mixing (FWM) of rubidium atoms. The simplified collective-steering criterion is introduced using the Coffman-Kundu-Wootters monogamy relation. Moreover, by actively adjusting the parametric gains, the collective EPR steerability is optimized in our schemes. We find that the scale of collective steering can be extended by cascading more FWMs; in particular, introducing optical loss is useful for generating collective steering with more parties only in the asymmetry structure. Our results pave the way for the construction of quantum networks and provide a promising candidate for one-sided device-independent quantum cryptography among multiple users.