Quantum Secret Sharing And Controlled Teleportation

1. Quantum secret sharingA protocol of quantum secret sharing between multiparty and multiparty with four states ispresented. We show that this protocol can make the Trojan horse attack with a multi-photonsignal, the fake-signal attack with Einstein-Podolsky-Rosen pairs, the attack with single photons,and the attack with invisible photons to be nullification. In addition, we also give the upperbounds of the average success probabilities for dishonest agent eavesdropping encryption usingthe fake-signal attack with any two-particle entangled states.We also propose a quantum secret sharing scheme between m-party and n-party using threeconjugate bases, i.e. six states. A sequence of single photons, each of which is prepared in oneof the six states, is used directly to encode classical information in the quantum secret sharingprocess. In this scheme, each of all m members in group 1 choose randomly their own secret keyindividually and independently, and then directly encode their respective secret information onthe states of single photons via unitary operations, then the last one (the mth member of group1) sends 1/n of the resulting qubits to each of group 2. By measuring their respective qubits,all members in group 2 share the secret information shared by all members in group 1. Thesecret message shared by group 1 and group 2 in such a way that neither subset of each groupnor the union of a subset of group 1 and a subset of group 2 can extract the secret message, buteach whole group (all the members of each group) can. The scheme is asymptotically 100% ine?ciency. It makes the Trojan horse attack with a multi-photon signal, the fake-signal attackwith Einstein-Podolsky-Rosen pairs, the attack with single photons, and the attack with invisiblephotons to be nullification. We show that it is secure and has an advantage over the one basedon two conjugate bases. We also give the upper bounds of the average success probabilitiesfor dishonest agent eavesdropping encryption using the fake-signal attack with any two-particleentangled states. This protocol is feasible with present-day technique.Another scheme of quantum secret sharing between Alices'group and Bobs'group withsingle photons and unitary transformations has been put forward. In the protocol, one memberin Alices'group prepares a sequence of single photons in one of four di?erent states, whileother members directly encode their information on the sequence of single photons via unitaryoperations, after that the last member sends the sequence of single photons to Bobs'group. ThenBobs except for the last one do work similarly. Finally last member in Bobs'group measures the qubits. If Alices and Bobs guaranteed the security of quantum channel by some tests, thenthe qubit states sent by last member of Alices'group can be used as key bits for secret sharing.It is shown that this scheme is safe.2. Controlled teleportationThe probability of successfully controlled teleporting an unknown qubit using a generalthree-particle state is investigated. We give the analytic expressions of maximal probabilitiesof successfully controlled teleporting an unknown qubit via every kinds of tripartite states in-cluding a tripartite Greenberger-Horne-Zeilinger state and a tripartite W-state, respectively.Besides, another kind of localizable entanglement is also determined. Furthermore, we obtainthe su?cient and necessary condition that a three-qubit state can be collapsed to an Einstein-Podolsky-Rosen pair by a measurement on one qubit, and characterize the three-qubit statesthat can be used as quantum channel for controlled teleporting a qubit of unknown informationwith unit probability 1 and with unit fidelity.3. An implementation of a positive operator valued measureAn implementation of the positive operator valued measure (POVM) is given. In particular,we give a decomposition of the unitary operation which plays an important role in the imple-mentation of the positive operator valued measure. By using this POVM one can realize theprobabilistic teleportation of an unknown two-particle state.4. Capacity of a simultaneous quantum secure direct communication schemebetween the central party and other M partiesWe analyze the capacity of a simultaneous quantum secure direct communication schemebetween the central party and other M parties via M + 1-particle Greenberger-Horne-Zeilingerstates and swapping quantum entanglement. It is shown that the encoding scheme should besecret if other M parties wants to transmit M + 1 bit classical messages to the center partysecretly. However when the encoding scheme is announced publicly, we prove that the capacityof the scheme in transmitting the secret messages is 2 bits, no matter how M is.