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.
As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and are generalized to multi-particle systems. First we describe two transformations of the shared resources for teleportation and superdense coding, which allow many new protocols from some known ones for that. As an application of these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. As another application, we find that state |W 123 = 1 2 (|100 123 + |010 123 + √ 2|001 123 ) can be used to transmit three classical bits by sending two qubits, which was considered to be impossible by P. Agrawal and A. Pati [Phys. Rev. A to be published]. We generalize the states of W-class to multi-qubit systems and multi-particle systems with higher dimension. We propose two protocols for teleportation and superdense coding by using W-states of multi-qubit systems that generalize the protocols by using |W 123 proposed by P. Agrawal and A. Pati. We obtain an optimal way to partition some W-states of multi-qubit systems into two subsystems, such that the entanglement between them achieves maximum value.
Two quantum finite automata are equivalent if for any input string x the two automata accept x with equal probability. In this paper, we focus on determining the equivalence for 1-way quantum finite automata with control language (CL-1QFAs) defined by Bertoni et al and measure-many 1-way quantum finite automata (MM-1QFAs) introduced by Kondacs and Watrous. It is worth pointing out that although Koshiba tried to solve the same problem for MM-1QFAs, we show that his method is not valid, and thus determining the equivalence between MM-1QFAs is still left open until this paper appears. More specifically, we obtain that:(i) Two CL-1QFAs A 1 and A 2 with control languages (regular languages) L 1 and L 2 , respectively, are equivalent if and only if they are (c 1 n 2 1 + c 2 n 2 2 − 1)-equivalent, where n 1 and n 2 are the numbers of states in A 1 and A 2 , respectively, and c 1 and c 2 are the numbers of states in the minimal DFAs that recognize L 1 and L 2 , respectively. Furthermore, if L 1 and L 2 are given in the form of DFAs, with m 1 and m 2 states, respectively, then there exists a polynomial-time algorithm running in time O((m 1 n 2 1 + m 2 n 2 2 ) 4 ) that takes as input A 1 and A 2 and determines whether they are equivalent.(ii) Two MM-1QFAs A 1 and A 2 with n 1 and n 2 states, respectively, are equivalent if and only if they are (3n 2 1 + 3n 2 2 − 1)-equivalent. Furthermore, there is a polynomial-time algorithm running in time O((3n 2 1 +3n 2 2 ) 4 ) that takes as input A 1 and A 2 and determines whether A 1 and A 2 are equivalent.
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