Unconditional security of entanglement-based continuous-variable quantum secret sharing

Kogias, Ioannis; Yu, X. D.; He, Qiongyi; Adesso, Gerardo

doi:10.1103/physreva.95.012315

Cited by 148 publications

(108 citation statements)

References 66 publications

(108 reference statements)

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“…If this is the case, Bob is said to steer Alice's state. In practical applications [26,27], steering is important when Alice does not trust Bob, since it allows Alice to verify that strong quantum correlations are present and that Bob conveyed the correct measurement outcomes. The only condition is that Alice should trust her own setup.…”

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confidence: 99%

Remote Generation of Wigner Negativity through Einstein-Podolsky-Rosen Steering

Walschaers

Treps

2020

Phys. Rev. Lett.

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Negativity of the Wigner function is seen as a crucial resource for reaching a quantum computational advantage with continuous variable systems. However, these systems, while they allow for the deterministic generation of large entangle states, require an extra element such as photon subtraction to obtain such negativity. Photon subtraction is known to affect modes beyond the one where the photon is subtracted, an effect which is governed by the correlations of the state. In this manuscript, we build upon this effect to remotely prepare states with Wigner-negativity. More specifically, we show that photon subtraction can induce Wigner-negativity in a correlated mode if and only if that correlated mode can perform Einstein-Podolsky-Rosen steering in the mode of subtraction.Manipulating networks is at the heart of information processing and communication. Hence, the growing interest in a quantum internet [1, 2] is a logical step in the developments of quantum technologies. The key idea of such a quantum network, be it for communication or for distributed computation, is to connect a large number of nodes via quantum entanglement [3,4]. A platform that is particularly promising for such applications is continuous-variable quantum optics, where large entangled graph states can be deterministically produced [5][6][7][8][9]. Even though this allows us to produce intricate quantum networks, the resulting Gaussian quantum states still have a positive Wigner function.Negativity of the Wigner function has been identified as a necessary ingredient for implementing processes that cannot be simulated efficiently with classical resources [10,11], and is therefore an essential resource [12,13] to achieve a quantum advantage. In networked quantum technologies it is, thus, crucial to generate and distribute Wigner-negativity in the nodes of a quantum network. In this spirit we focus here on the remote generation of Wigner-negativity, such that operations in one node of a quantum network create negativity in the Wigner function of another node while upholding the entanglement in the quantum network.Photon subtraction [14-16] is a natural candidate for such operation. In previous work, we showed that the subtraction of a photon causes an interplay between correlations and non-Gaussian features [17]. In the specific case of graph states, it was shown that non-Gaussian properties, induced by photon subtraction, propagate through the system [18,19], however it is far from clear whether this mediated non-Gaussianity has quantum features (see also [20]). Hence, here we turn the question around, and ask what type of correlations are required to remotely generate negativity of the Wigner function through photon subtraction. We show that Einstein-Podolsky-Rosen (EPR) steering [21-25] is a necessary and sufficient condition.In its essence, EPR steering focusses on the the structure of conditional quantum probabilities: when Alice and Bob share a quantum state, Bob can perform measurements on his part of the state and Alice can condition her...

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confidence: 99%

Remote Generation of Wigner Negativity through Einstein-Podolsky-Rosen Steering

Walschaers

Treps

2020

Phys. Rev. Lett.

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“…QSS can be implemented when the players are sepa-rated in a local quantum network and collaborate to decode the secret sent by the dealer who owns the other one mode [31]. In this case, the dealer must not be steered by any one of two players; only the collective steerability is needed.…”

Section: Discussionmentioning

confidence: 99%

“…The graph state is a basic resource in quantum information and quantum computation. For example, multiparty Greenberger-Horne-Zeilinger (GHZ) state and cluster state have been used in quantum communication [31][32][33][34][35] and one-way quantum computation [36,37], respectively.…”

Section: Introductionmentioning

confidence: 99%

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

et al. 2019

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Einstein-Podolsky-Rosen (EPR) steering, as one of the most intriguing phenomenon of quantum mechanics, is a useful quantum resource for quantum communication. Understanding the type of EPR steering in a graph state is the basis for application of it in a quantum network. In this paper, we present EPR steering in a Gaussian weighted graph state, including a linear tripartite and a four-mode square weighted graph state. The dependence of EPR steering on weight factor in the weighted graph state is analyzed. Gaussian EPR steering between two modes of a weighted graph state is presented, which does not exist in the Gaussian cluster state (where the weight factor is unit). For the four-mode square Gaussian weighted graph state, EPR steering between one and its two nearest modes is also presented, which is absent in the four-mode square Gaussian cluster state. We also show that Gaussian EPR steering in a weighted graph state is also bounded by the Coffman-Kundu-Wootters monogamy relation. The presented results are useful for exploiting EPR steering in a Gaussian weighted graph state as a valuable resource in multiparty quantum communication tasks.I.

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“…By choosing an appropriate beam splitting ratio, the additional loss introduced by each player's system can be extremely small, making the protocol extendable to a large number of players. Furthermore, by extending the ideas introduced in [15], we prove the general security of the proposed protocol against both eavesdroppers and dishonest players in the presence of high channel loss. This paper is organized as follows: In Section II, we present details of the proposed QSS scheme and provide a general security proof.…”

Section: Introductionmentioning

confidence: 88%

“…The security analysis of a QSS protocol is typically more involved than that of QKD. The general security proof against both eavesdroppers in the channels and dishonest players only appeared recently [15]. In [15], the dealer prepares a multiparty continuous-variable entangled state, keeps one mode and distributes the other modes to the players.…”

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confidence: 99%

Quantum secret sharing using weak coherent states

Grice

2019

Phys. Rev. A

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Secret sharing allows a trusted party (the dealer) to distribute a secret to a group of players, who can only access the secret cooperatively. Quantum secret sharing (QSS) protocols could provide unconditional security based on fundamental laws in physics. While the general security proof has been established recently in an entanglement-based QSS protocol, the tolerable channel loss is unfortunately rather small. Here we propose a continuous variable QSS protocol using conventional laser sources and homodyne detectors. In this protocol, a Gaussian-modulated coherent state (GMCS) prepared by one player passes through the secure stations of the other players sequentially, and each of the other players injects a locally prepared, independent GMCS into the circulating optical mode. Finally, the dealer measures both the amplitude and the phase quadratures of the receiving optical mode using double homodyne detectors. Collectively, the players can use their encoded random numbers to estimate the measurement results of the dealer and further generate a shared key. We prove the unconditional security of the proposed protocol against both eavesdroppers and dishonest players in the presence of high channel loss, and discuss various practical issues. a

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Unconditional security of entanglement-based continuous-variable quantum secret sharing

Cited by 148 publications

References 66 publications

Remote Generation of Wigner Negativity through Einstein-Podolsky-Rosen Steering

Remote Generation of Wigner Negativity through Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen steering in Gaussian weighted graph states

Quantum secret sharing using weak coherent states

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