Hierarchical and probabilistic quantum state sharing via a non-maximally entangled |χ〉state

A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X） state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice＇s secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.

Probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and its application in quantum state sharing

This paper presents a scheme for probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel. The sender Alice first teleports the coefficients of the unknown state to the receiver Bob, and then Bob reconstructs the state with an auxiliary particle and some unitary operations if the teleportation succeeds. This scheme has the advantage of transmitting much less particles for teleporting an arbitrary GHZ-class state than others. Moreover, it discusses the application of this scheme in quantum state sharing.

A rational quantum state sharing protocol with semi-off-line dealer

A rational quantum state sharing protocol with the semi-off-line dealer is proposed.Firstly,the dealer Alice shares an arbitrary two-particle entangled state with the players by Einstein-Podolsky-Rosen(EPR)pairs and Greenberger-Horne-Zeilinger(GHZ)states.The EPR pairs are prepared by Charlie instead of the dealer,reducing the workload of the dealer.Secondly,all players have the same probability of reconstructing the quantum state,guaranteeing the fairness of the protocol.In addition,the dealer is semi-off-line,which considerably reduces the information exchanging between the dealer and the players.Finally,our protocol achieves security,fairness,correctness,and strict Nash equilibrium.

Quantum state sharing of an arbitrary qudit state by using nonmaximally generalized GHZ state

We present a scheme for quantum state sharing of an arbitrary qudit state by using nonmaximally entangled generalized Greenberger-Horne-Zeilinger （GHZ） states as the quantum channel and generalized Bell-basis states as the joint measurement basis. We show that the probability of successful sharing an unknown qudit state depends on the joint measurements chosen by Alice. We also give an expression for the maximally probability of this scheme.

Controlled quantum state sharing of arbitrary two-qubit states with five-qubit cluster states

In this paper, we propose a controlled quantum state sharing scheme to share an arbitrary two-qubit state using a five-qubit cluster state and the Bell state measurement. In this scheme, the five-qubit cluster state is shared by a sender （Alice）, a controller （Charlie）, and a receiver （Bob）, and the sender only needs to perform the Bell-state measurements on her particles during the quantum state sharing process, the controller performs a single-qubit projective measurement on his particles, then the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his particles after he has known the measured results of the sender and the controller.

Deterministic all-optical quantum state sharing

Quantum state sharing,an important protocol in quantum information,can enable secure state distribution and reconstruction when part of the information is lost.In(k,n)threshold quantum state sharing,the secret state is encoded into n shares and then distributed to n players.The secret state can be reconstructed by any k players(k>n∕2),while the rest of the players get nothing.In the continuous variable regime,the implementation of quantum state sharing needs the feedforward technique,which involves opticelectro and electro-optic conversions.These conversions limit the bandwidth of the quantum state sharing.Here,to avoid the optic-electro and electro-optic conversions,we experimentally demonstrate(2,3)threshold deterministic all-optical quantum state sharing.A low-noise phase-insensitive amplifier based on the four-wave mixing process is utilized to replace the feedforward technique.We experimentally demonstrate that any two of three players can cooperate to implement the reconstruction of the secret state,while the rest of the players cannot get any information.Our results provide an all-optical platform to implement arbitrary(k,n)threshold deterministic all-optical quantum state sharing and pave the way to construct the all-optical broadband quantum network.

Several teleportation schemes of an arbitrary unknown multi-particle state via different quantum channels

We first provide four new schemes for two-party quantum teleportation of an arbitrary unknown multi-particle state by using three-, four-, and five-particle states as the quantum channel, respectively. The successful probability and fidelity of the four schemes reach 1. In the first two schemes, the receiver can only apply one of the unitary transformations to reconstruct the original state, making it easier for these two schemes to be directly realized. In the third and fourth schemes, the sender can preform Bell-state measurements instead of multipartite entanglement measurements of the existing similar schemes, which makes real experiments more suitable. It is found that the last three schemes may become tripartite controlled teleportation schemes of teleporting an arbitrary multi-particle state after a simple modification. Finally, we present a new scheme for three-party sharing an arbitrary unknown multi-particle state. In this scheme, the sender first shares three three-particle GHZ states with two agents. After setting up the secure quantum channel, an arbitrary unknown multi-particle state can be perfectly teleported if the sender performs three Bell-state measurements, and either of two receivers operates an appropriate unitary transformation to obtain the original state with the help of other receiver＇s three single-particle measurements. The successful probability and fidelity of this scheme also reach 1. It is demonstrated that this scheme can be generalized easily to the case of sharing an arbitrary unknown multi-particle state among several agents.