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By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states. [ABSTRACT FROM AUTHOR]

Gao et al. have studied the controlled remote preparation of arbitrary two- and three-qubit states via the Brown state as the entangled channel. But these schemes are considered in ideal environment. In this paper, we take the scheme of preparing an arbitrary two-qubit state as an example and reinvestigate it in five-type noises: the bit flip, phase flip, bit-phase flip, phase-damping and amplitude-damping noise. The fidelity is adopted to describe how close the output state with the prepared state are. It is found that the fidelity of the output state is dependent on the coefficients of the prepared state and the noise parameter in five-type noises. Interestingly, the fidelity is irrelated to the participators’ measurement results except in the amplitude-damping noise. [ABSTRACT FROM AUTHOR]

By constructing sets of ingenious measurement bases at the sender's and the controller's locations, we devise two schemes to realize the controlled remote preparation of an arbitrary four-qubit χ-state via partially entangled quantum resource. The success probabilities of the proposed schemes are 50 % and 100 %, respectively. It means that the success probabilities are independent of the coefficients of the entangled channel. [ABSTRACT FROM AUTHOR]

The ability to prepare arbitrary quantum state is the holy grail of quantum information technology. Previous schemes focus on circuit complexity using implicit decomposition schemes for global evolutions and are difficult in quantum experiments because the generation circuit can be completed for given coefficients each time. One protocol is firstly proposed in this paper in order to deterministically generate arbitrary four-qubit states with any coefficients. In order to complete this scheme with present physical techniques, we present an explicit quantum circuit with unknown coefficients of prepared states using elementary quantum gates. The key of our scheme is constructing the Cartan KAK decomposition of special transformations in $$SO(4)$$ and $$SO(8)$$ . And then, this protocol is extended to arbitrary five-qubit states and six-qubit states. [ABSTRACT FROM AUTHOR]

Two schemes via different entangled resources as the quantum channel are proposed to realize remote preparation of an arbitrary four-particle $$\chi $$ -state with high success probabilities. To design these protocols, some useful and general measurement bases are constructed, which have no restrictions on the coefficients of the prepared states. It is shown that through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the original state can be prepared with the probability 50 and 100 %, respectively. And for the first scheme, the special cases of the prepared state that the success probability reaches up to 100 % are discussed by the permutation group. Furthermore, the present schemes are extended to the non-maximally entangled quantum channel, and the classical communication costs are calculated. [ABSTRACT FROM AUTHOR]

In this work, novel schemes for joint remote state preparation are presented, which involve N senders and 2 receivers as well as N senders and 3 receivers. The receivers can simultaneously reconstruct different qubit states containing the joint information from all senders. Compared with the protocols proposed by Su et al. (Int J Quantum Inf 10:1250006 (), the information of the prepared states in our schemes is distributed in a different way. Our protocols can be applied not only to states with real parameters but also ones with complex parameters. Moreover, the N-to-2 protocol is suitable for general qubit states besides equatorial states, and the receivers need not to perform any measurements and CNOT gates to reconstruct the states. [ABSTRACT FROM AUTHOR]

Two novel schemes via different entanglement resources are put forward to remotely preparing a five-qubit Brown-type state with high probabilities. To design the schemes, some useful measurement bases with the aid of Hurwitz matrix equation are constructed, which have no restrictions on the coefficients of the prepared state. Through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the remote preparation can be realized with the probability 50% and 100% in general case, respectively. To improve the probability, the special ensembles of the prepared state that the success probability reaches up to 100% are discussed for the first scheme by the permutation group. Furthermore, the present schemes are extended to the nonmaximally entangled quantum channel. [ABSTRACT FROM AUTHOR]

The application of χ state are investigated in remote state preparation (RSP). By constructing useful measurement bases with the aid of Hurwitz matrix equation, we propose several RSP schemes of arbitrary two- and three-qubit states via the χ state as the entangled resource. It is shown that the original state can be successfully prepared with the probability 100% and 50% for real coefficients and complex coefficients, respectively. For the latter case, the special ensembles with unit success probability are discussed by the permutation group. It is worth mentioning that the novel measurement bases have no restrictions on the coefficients of the prepared state, which means that the proposed schemes are more applicable. [ABSTRACT FROM AUTHOR]