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International Journal of Quantum Information

GENERALIZED QUANTUM TWO-QUBIT STATE SHARING VIA POSITIVE OPERATOR-VALUED MEASURE

Zhang-Yin Wang, Xingqiang Yang

Published Feb 1, 2011• 4 citations
Publisher

Abstract

By using a proper positive operator-valued measure (POVM), we present a new scheme for probabilistically implementing quantum state sharing of an arbitrary unknown two-qubit state with two non-maximally entangled three-qubit states. In this paper, the sender Alice averagely partitions its unknown original state with two Bell-state measurements and publishes her measurement results via a classical channel. Then by performing a proper POVM, it is shown that either of the two agents Bob or Charlie can recover the original state in a probabilistic manner provided that he/she gets another one's help. Lastly, we concisely generalize the tripartite scheme to a multi-party case.

DOI
10.1142/s0219749911007630

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By using a proper positive operator-valued measure (POVM), we present a new scheme for probabilistically implementing quantum state sharing of an arbitrary unknown two-qubit state with two non-maximally entangled three-qubit states. In this paper, the sender Alice averagely partitions its unknown original state with two Bell-state measurements and publishes her measurement results via a classical channel. Then by performing a proper POVM, it is shown that either of the two agents Bob or Charlie can recover the original state in a probabilistic manner provided that he/she gets another one's help. Lastly, we concisely generalize the tripartite scheme to a multi-party case.
In this paper, by using a proper positive operator-valued measurement, we propose a new tripartite scheme for probabilistically implementing quantum state sharing of an arbitrary unknown three-qubit state with two non-maximally entangled states, one is four-qubit state, another is three-qubit state. In the scheme, the Boss Alice partitions her unknown original state with two Bell-state measurements and a single-qubit projective measurement. Then she publishes her measurement results via a classical channel. With an agent Charlie's help, another agent Bob can recover the original state in probabilistic manner by performing a proper POVM.
A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled |χ〉 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.
Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements, and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement (POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.
We present a new scheme for investigating the usefulness of non-maximally entangled states for multi-party quantum state sharing in a simple and elegant manner. In our scheme, the sender, Alice shares n various probabilistic channels composed of non-maximally entangled states with n agents in a network. Our protocol involves only Bell-basis measurements, single qubit measurements, and a two-qubit unitary transformation operated by free optional agents. Our scheme is a more convenient realization because no other multipartite joint measurements are needed. Furthermore, in our scheme various probabilistic channels lessen the requirement for quantum channels, which makes it more practical for physical implementation.
Abstract We propose a novel scheme to probabilistically transmit an arbitrary unknown two-qubit quantum state via Positive Operator-Valued Measurement with the help of two partially entangled states. In this scheme, the teleportation with two senders and two receives can be realized when the information of non-maximally entangled states is only available for the senders. Furthermore, the concrete implementation processes of this proposal are presented, meanwhile the classical communication cost and the successful probability of our scheme are calculated.
We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n − 1 auxiliary particles in the initial state |0⟩, applies Hadamard (H) gate and Controlled-Not (CNOT) gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers (i.e., other n − 1 agents), where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.