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秘密共享是经典密码理论中的一个重要实现 ,是指将一个秘密由一个集团所拥有 ,集团中的任何一个成员都能且仅能在别的成员同意合作的情况下得到此秘密。在量子密码理论中也可以实现量子秘密共享 ,这也是量子密码理论的重要组成部分。由于秘密共享至少涉及三方通信 :信息提供方和至少两个信息共享方。在这里我们用三粒子纠缠态(D .M .Greenberger ,M .A .Horne ,A .Shimony ,andA .Zeilinger ,Am .J .Phys .1990 ,58:1131) (非最大纠缠态 )来模拟研究量子秘密共享。已有的方案如M .Hillery (M .Hillery ,V .BuzekandA .Berthiaume ,Phys .Rev .1999,A59:182 9)和SomshubhroBandyopadhyay (SomshubhroBandyopadhyay ,quant-ph/ 0 0 0 2 0 32 )提出的利用添加辅助粒子 ,再作POVM (PositiveOperatorValuedMeasurement)测量使得将信息提供方 (Alice)发给共享集团(Bob ,Charlie)的信息可以以一定的概率由Bob和Charlie之一得到 ,并由于初始态非最大纠缠 ,所以要计算出最后一方得到信息的概率。我们的方案是利用Bob添加辅助粒子 ,并作幺正变换实现态的演化 ,以辅助粒子作为成功演化的标识 ,通过对辅助粒子的末态作VonNeumann测量 ,从而以一定概率使Charlie得到共享的信息 ,最后计算的概率和用POVM方案是一样的
Secret sharing is an important realization of classical cryptography, which means that a secret is owned by a group, and any member of the group can and can only get this secret if the other members agree to cooperate. Quantum cryptography can also be achieved quantum secret sharing, which is an important part of quantum cryptography. Because secret sharing involves at least three-way communication: the information provider and at least two parties to information sharing. Here we use the three-particle entangled state (D.M. Greenberger, M.A.Horne, A.Shimony, and A.Zeilinger, Am. J. Phys. 1990, 58: 1131) (nonmaximally entangled states) Quantum secret sharing. Existing protocols such as those proposed by M. Hillery (M. Hillery, V. Buzek and A. Berthiaume, Phys. Rev. 1999, A59: 182 9) and Somshubhro Bandyopadhyay (Somshubhro Bandyopadhyay, quant- ph / 0 0 0 2 0 32) Auxiliary particles, then POVM (Positive Operation Measured Value) measurement make information sent by Alice to Bob (Charlie) can be obtained by one of Bob and Charlie with a certain probability. Due to the non-maximal initial entanglement, So to calculate the probability of the last party to get the information. Our scheme is to use Bob to add auxiliary particles and to realize unitary transformation to realize the evolution of states to assist the particles as a marker of successful evolution. By using the Von Neumann measurement of the final state of the auxiliary particles, Charlie can obtain the shared information with a certain probability , The final calculation of the probability and the POVM program is the same