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arXiv:0906.1866 · Physical Review A

Semiquantum secret sharing using entangled states

Qin Li, Wai Hong Chan, Dongyang Long

Published Aug 4, 2010• 187 citations
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Abstract

Secret sharing is a procedure for sharing a secret among a number of participants such that only the qualified subsets of participants have the ability to reconstruct the secret. Even in the presence of eavesdropping, secret sharing can be achieved when all the members are quantum. So what happens if not all the members are quantum? In this paper, we propose two semiquantum secret sharing protocols by using maximally entangled Greenberger-Horne-Zeilinger-type states in which quantum Alice shares a secret with two classical parties, Bob and Charlie, in a way that both parties are sufficient to obtain the secret, but one of them cannot. The presented protocols are also shown to be secure against eavesdropping.

DOI
10.1103/physreva.82.022303

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Secret sharing is a procedure for sharing a secret among a number of participants such that only the qualified subsets of participants have the ability to reconstruct the secret. Even in the presence of eavesdropping, secret sharing can be achieved when all the members are quantum. So what happens if not all the members are quantum? In this paper, we propose two semiquantum secret sharing protocols by using maximally entangled Greenberger-Horne-Zeilinger-type states in which quantum Alice shares a secret with two classical parties, Bob and Charlie, in a way that both parties are sufficient to obtain the secret, but one of them cannot. The presented protocols are also shown to be secure against eavesdropping.
Recently, Boyer et al. presented a novel semiquantum key distribution protocol [ Phys. Rev. Lett. 99 (2007) 140501 ] by using four quantum states, each of which is randomly prepared in the Z or X basis. Here we present a semi-quantum key distribution protocol by using maximally entangled states in which quantum Alice shares a secret key with classical Bob. Quantum Alice has the ability to prepare Bell states and perform Bell basis or computational basis measurement. Classical Bob is restricted to measuring, preparing a particle in the computational basis, reflecting or reordering the particles. The qubit efficiency of the protocol improves to 50% and the protocol can be modified to a measure-resend protocol or a protocol without quantum memory. We also show that the protocol is secure against eavesdropping.
Since the first quantum secret sharing protocol based on Greenberger–Horne–Zeilinger (GHZ) states was presented by Hillery et al, dozens of quantum secret sharing protocols based on different entangled states (e.g. Bell states, d-level Bell states and GHZ states, etc) and product states have been developed. In this paper, we present a quantum secret sharing protocol, in which the genuinely maximally entangled six-qubit states, which was found recently by Borras et al, are used. An ordinary entangled state such as a Bell state or a GHZ state, etc can be used to share at most only one bit. However, according to our protocol, Alice can share three bits among three parties by a six-qubit state, which shows that our protocol is more efficient than any previous protocol.
Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Extending the idea of “semiquantum” to other tasks of quantum information processing is of interest and worth considering. In this article, we consider the issue of semi-quantum secret sharing where a quantum participant Alice can share a secret key with two classical participants Bobs. After analyzing the existing protocol, we propose a new protocol of semi-quantum secret sharing. Our protocol is more realistic, since it utilizes product states instead of entangled states. We prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice. 1
Based on the assumption of a perfect qubit, Boyer et al. proposed a novel semiquantum key distribution protocol [Phys. Rev. Lett. 99 (2007) 140501], in which quantum Alice shares a secret key with classical Bob. In this paper, we use Bell states to propose a multiparty semiquantum secret sharing (MSQSS) protocol, in which only the boss is quantum and all agents are classical. Classical agents are restricted to performing measurements in a computational basis and rearranging orders of qubits. Unless all classical agents collaborate, no subset of them can obtain the secret of the quantum boss. Also, we show that this proposed protocol is secure against eavesdropping.
In single-qubit quantum secret sharing, a secret is shared between NNN parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all NNN parties in sequence; the secret is encoded in the first participant's preparation of the qubit state and the subsequent participants' choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol's security against eavesdropping attack under common experimental conditions: a lossy channel for photon transmission, and imperfect preparation of the initial qubit state. A protocol which exploits entanglement between photons, rather than simply polarization correlation, is more robustly secure. We implement the entanglement-based secret-sharing protocol with 87% secret-sharing fidelity, limited by the purity of the entangled state produced by our present apparatus. We demonstrate a photon-number splitting eavesdropping attack, which achieves no success against the entanglement-based protocol while showing the predicted rate of success against a correlation-based protocol.