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arXiv:1212.2270 · Physical Review Letters

Genuine Multipartite Einstein-Podolsky-Rosen Steering

Qiongyi He, M. D. Reid

Published Dec 18, 2013• 252 citations
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Abstract

We develop the concept of genuine N-partite Einstein-Podolsky-Rosen (EPR) steering. This nonlocality is the natural multipartite extension of the original EPR paradox. Useful properties emerge that are not guaranteed for genuine multipartite entangled states. In particular, there is a close link with the task of one-sided, device-independent quantum secret sharing. We derive inequalities to demonstrate multipartite EPR steering for Greenberger-Horne-Zeilinger and Gaussian continuous variable states in loophole-free scenarios.

DOI
10.1103/physrevlett.111.250403

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We develop the concept of genuine N-partite Einstein-Podolsky-Rosen (EPR) steering. This nonlocality is the natural multipartite extension of the original EPR paradox. Useful properties emerge that are not guaranteed for genuine multipartite entangled states. In particular, there is a close link with the task of one-sided, device-independent quantum secret sharing. We derive inequalities to demonstrate multipartite EPR steering for Greenberger-Horne-Zeilinger and Gaussian continuous variable states in loophole-free scenarios.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
Einstein-Podolsky-Rosen (EPR) steering demonstrates that two parties share entanglement even if the measurement devices of one party are untrusted. Here, going beyond this bipartite concept, we develop a novel formalism to explore a large class of EPR steering from generic multipartite quantum systems of arbitrarily high dimensionality and degrees of freedom, such as graph states and hyperentangled systems. All of these quantum characteristics of genuine high-order EPR steering can be efficiently certified with few measurement settings in experiments. We faithfully demonstrate for the first time such generality by experimentally showing genuine four-partite EPR steering and applications to universal one-way quantum computing. Our formalism provides a new insight into the intermediate type of genuine multipartite Bell nonlocality and potential applications to quantum information tasks and experiments in the presence of untrusted measurement devices.
Following previous work, we distinguish between genuine NNN-partite entanglement and full NNN-partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous-variable (position and momentum) measurements. Our criteria are similar but different to those based on the van Loock--Furusawa inequalities, which detect full NNN-partite inseparability. We explain how the criteria can be used to detect the genuine NNN-partite entanglement of continuous variable states generated from squeezed and vacuum state inputs, including the continuous-variable Greenberger-Horne-Zeilinger state, with explicit predictions for up to N=9N=9N=9. This makes our work accessible to experiment. For N=3N=3N=3, we also present criteria for tripartite Einstein-Podolsky-Rosen (EPR) steering. These criteria provide a means to demonstrate a genuine three-party EPR paradox, in which any single party is steerable by the remaining two parties.
We propose criteria and experimental strategies to realise the Einstein-Podolsky-Rosen (EPR) steering nonlocality. One-way steering can be obtained where there is asymmetry of thermal noise on each system. We also present EPR steering inequalities that act as signatures and suggest how to optimise EPR correlations in specific schemes so that the genuine multipartite EPR steering nonlocality (EPR paradox) can also possibly be realised. The results presented here also apply to the spatially separated macroscopic atomic ensembles.
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.
Multipartite Einstein-Podolsky-Rosen (EPR) steering is a useful quantum resource for quantum communication in quantum networks. It has potential applications in secure quantum communication, such as one-sided device-independent quantum key distribution and quantum secret sharing. By distributing optical modes of a multipartite entangled state to space-separated quantum nodes, a local quantum network can be established. Based on the existing multipartite EPR steering in a local quantum network, secure quantum communication protocol can be accomplished. In this manuscript, we present swapping schemes for EPR steering between two space-separated Gaussian multipartite entangled states, which can be used to connect two space-separated quantum networks. Two swapping schemes, including the swapping between a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state and an EPR entangled state and that between two tripartite GHZ entangled states, are analyzed. Various types of EPR steering are presented after the swapping of two space-separated independent multipartite entanglement states without direct interaction, which can be used to implement quantum communication between two quantum networks. The presented schemes provide technical reference for more complicated quantum networks with EPR steering.