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

doi:10.1088/1674-1056/23/1/010304

Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 10304-010304.doi: 10.1088/1674-1056/23/1/010304

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

彭家寅^{a b}, 柏明强^a, 莫智文^a

a College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China;
b School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China

收稿日期:2013-04-25 修回日期:2013-06-08 出版日期:2013-11-12 发布日期:2013-11-12
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11071178) and the Research Foundation of the Education Department of Sichuan Province, China (Grant No. 12ZB106).

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

Peng Jia-Yin (彭家寅)^{a b}, Bai Ming-Qiang (柏明强)^a, Mo Zhi-Wen (莫智文)^a

a College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China;
b School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China

Received:2013-04-25 Revised:2013-06-08 Online:2013-11-12 Published:2013-11-12
Contact: Peng Jia-Yin E-mail:pengjiayin62226@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11071178) and the Research Foundation of the Education Department of Sichuan Province, China (Grant No. 12ZB106).

摘要/Abstract

摘要： 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.

关键词: χ> state, hierarchical quantum state sharing, asymmetetric distribution, positive operator-valued measurement

Abstract: 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.

Key words: χ> state, hierarchical quantum state sharing, asymmetetric distribution, positive operator-valued measurement

中图分类号: (Quantum communication)

03.67.Hk

03.67.Dd (Quantum cryptography and communication security) 03.65.Ud (Entanglement and quantum nonlocality)

彭家寅, 柏明强, 莫智文. Hierarchical and probabilistic quantum state sharing via a non-maximally entangled |χ> state[J]. Chin. Phys. B, 2014, 23(1): 10304-010304.

Peng Jia-Yin (彭家寅), Bai Ming-Qiang (柏明强), Mo Zhi-Wen (莫智文). Hierarchical and probabilistic quantum state sharing via a non-maximally entangled |χ> state[J]. Chin. Phys. B, 2014, 23(1): 10304-010304.

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

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

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