Multiparty hierarchical quantum-information splitting

Abstract

We propose a scheme for multiparty hierarchical quantum-information splitting (QIS) with a multipartite entangled state, where a boss distributes a secret quantum state to two grades of agents asymmetrically. The agents who belong to different grades have different authorities for recovering boss's secret. Except for boss's Bell-state measurement, no nonlocal operation is involved. The presented scheme is also shown to be secure against eavesdropping. Such a hierarchical QIS is expected to find useful applications in the field of modern multipartite quantum cryptography. A fundamental ingredient for implementation of quantum technologies is the ability to faithfully transmit quantum states among quantum mechanical systems which are even far apart. Quantum-information splitting (QIS, also be referred to as quantum-secret sharing or quantum-state sharing in the literature), first introduced by Hillery, Bužek, and Berthiaume (HBB) [1], is a typical way for quantum state transfer, in which a secret quantum state is distributed by quantum teleportation [2] from a boss to more than one agents so that any one of them can recover the state with assistance of the others. QIS is a generalization of classical-secret sharing to quantum scenario. Classical-secret sharing is one of the most important information-theoretically secure cryptographic protocols and is germane to online auctions, electronic voting, shared electronic banking, cooperative activation of bombs, and so on. Also, QIS has extensive applications in quantum-information science, such as creating joint checking accounts containing quantum money [3], secure distributed quantum computation [4,5], and so on. KeywordsIn the original HBB QIS proposal with the quantum channel being a three-qubit Greenberger-Horne-Zeilinger (GHZ) state [6], the collaboration of two agents is implemented by means of classical communication about their single-particle measurement outcomes. This idea can be directly generalized to the case of N agents by using an (N + 1)-particle GHZ state, or by the way of Ref. [7]. These schemes are (N , N )-threshold schemes where all the N agents need collaborating in order to recover the secret state. Soon after, Cleve, Gottesman, and Lo (CGL) [8] proposed another type of QIS scheme with the idea of quantum error-correcting codes. The CGL scheme is a (K, N )-threshold scheme where K ([N/2] < K ≤ N ) of N agents can extract the quantum information of the original secret state by cooperation. The CGL QIS scheme, however, needs the cooperated agents to make nonlocal operations on their particles. That is, the K cooperated agents need to transmit their K particles to one laboratory and perform a collective operation (decoding operation) on them. In the last decade, both of the above two QIS ideas have triggered significant research activity (see, e.g., [9][10][11][12][13][14][15][16][17][18][19]), and some schemes have already been experimentally realized [20,21].A more general QIS scheme should involve the asymmetry between the powers of the differen...

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