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Jisuanji kexue yu tansuo

Quantum Secret Sharing of Classical Messages by Genuinely Maximally Entangled Six-Qubit State

Yinxiang Long

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Entanglement is an important resource which can be applied in quantum information processing. Now, Bell states and GHZ states have been widely used in quantum secret sharing. The genuinely maximally entangled six-qubit state, which was discovered by Borras recently and called as Borras state, has been shown to exhibit some excellent characters in quantum teleportation. By analyzing the structure of Borras state and making generalized Schmidt decomposition, this paper constructs a concrete protocol of quantum secret sharing, in which Alice can share two bits among her agents, if she shares a Borras state with her four agents in advance (each agent has one qubit, and Alice has two qubits).

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Entanglement is an important resource which can be applied in quantum information processing. Now, Bell states and GHZ states have been widely used in quantum secret sharing. The genuinely maximally entangled six-qubit state, which was discovered by Borras recently and called as Borras state, has been shown to exhibit some excellent characters in quantum teleportation. By analyzing the structure of Borras state and making generalized Schmidt decomposition, this paper constructs a concrete protocol of quantum secret sharing, in which Alice can share two bits among her agents, if she shares a Borras state with her four agents in advance (each agent has one qubit, and Alice has two qubits).
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.
In this paper, we show that any S(S = 1, 2, 3, 4, 5, 6) persons can unite to teleport min(S, 6 - S) qubits to the other 6 - S persons if they a priori share a maximally genuinely entangled six-qubit state introduced by Borras et al. [A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas and A. Plastino, J. Phys. A40 (2007) 13407]. Also, explicit protocols for perfectly teleporting arbitrary one-qubit state, two-qubit state as well as three-qubit state between arbitrary split of six partites are constructed. Moreover, to fulfil the protocol, either the senders or the receivers can make local operations individually in distant places.
We show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is transmitted via N qubits is also presented. We also show that this four(2N-)partite channel is equivalent to two(N) Bell states, which proves that we need two(N) Bell states to teleport a two(N) qubit system.
In this paper, a standard (3, 5)-threshold quantum secret sharing scheme is presented, in which any three of five participants can resume cooperatively the classical secret from the dealer, but one or two shares contain absolutely no information about the secret. Our scheme can be fulfilled by using the singular properties of maximally entangled 6-qubit states found by Borras. We analyze the scheme's security by several ways, for example, intercept-and-resend attack, entangle-and-measure attack, and so on. Compared with the other standard threshold quantum secret sharing schemes, our scheme needs neither to use d-level multipartite entangled states, nor to produce shares by classical secret splitting techniques, so it is feasible to be realized.