基于量子电路的门限量子秘密共享方案
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摘要
对(n, n)门限量子秘密共享方案参与者人数n为任意的情形(即不局限于n=4k+1?,k∈Z~+)进行了研究,根据量子电路作用在量子态上的性质构造了一个(n, n)门限量子秘密共享方案,进而由Clifford群门和T门组成的可证明安全的量子电路进行安全性评估。最后,对不诚实的参与者攻击进行了安全性分析。
We study a( n, n) threshold quantum secret sharing scheme, where the number of participants is arbitrary (the number of participants is not limited to n = 4 k +1, k ∈Z~+). And a threshold quantum secret sharing scheme is constructed according to the properties of quantum circuits acting on quantum states,in which the quantum circuit is a provably secure quantum circuit composed of Clifford group gates and T gates. Finally,we use the property of the quantum circuit to analyze the security against dishonest participant attacks.
We study a( n, n) threshold quantum secret sharing scheme, where the number of participants is arbitrary (the number of participants is not limited to n = 4 k +1, k ∈Z~+). And a threshold quantum secret sharing scheme is constructed according to the properties of quantum circuits acting on quantum states,in which the quantum circuit is a provably secure quantum circuit composed of Clifford group gates and T gates. Finally,we use the property of the quantum circuit to analyze the security against dishonest participant attacks.
引文
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[10]HAYASHI M,MORIMAE T.Verifiable measurementonly blind quantum computing with stabilizer testing[J].Physical Review Letters,2015,115(22):220502.DOI:10.1103/PhysRevLett.115.220502.
[11]DEUTSCH D,JOZSA R.Rapid Solution of Problems by Quantum Computation[R].Bristol:University of Bristol,1992.
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[22]HILLERY M,BUZEK V,BERTHIAUME A.Quantum secret sharing[J].Physical Review A,1999,59(3):1829-1834.
[23]CLEVE R,GOTTESMAN D,LO H K.How to share a quantum secret[J].Physical Review Letters,1999,83(3):648-651.DOI:10.1103/PhysRevLett.83.648.
[24]GOTTESMAN D.Theory of quantum secret sharing[J].Physical Review A,2000,61(4):192-193.DOI:10.1103/Phys-RevA.61.042311.
[25]ZHANG Z J,MAN Z X.Multiparty quantum secret sharing of classical messages based on entanglement swapping[J].Physical Review A,2005,72(3):15-19.DOI:10.1103/PhysRevA.72.022303.
[26]MARKHAM D,SANDER B C.Graph states for quantum secret sharing[J].Physical Review A,2008,78(4):042309.DOI:10.1103/PhysRevA.78.042309.
[27]DEUTSCH D,BARENCO A,EKERT A.Universality in quantum computation[J].Proceedings Mathematical&Physical Sciences,1995,449(1937):669-677.
[28]ZHOU X,LEUNG D W,CHUANG I L.Methodology for quantum logic gate constructions[J].Physical Review A,2000,62(5):052316.DOI:10.1103/Phys RevA.62.052316.
[29]OUYANG Y,TAN S H,ZHAO L,et al.Computing on quantum shared secrets[DB/OL].[2018-06-04].https://journals.aps.org/pra/pdf/10.1103/PhysRevA.96.052333.
[2]BROADBENT A,FITZSIMONS J,KASHEFI E.Universal blind quantum computation[C]//Foundations of Compute Science,2010,19(6):517-526.DOI:10.1109/FO-CS.2009.36.
[3]MORIMAE T,FUJII K.Blind topological measurementbased quantum computation[J].Nature Communications,2012,3(3):1036.DOI:10.1038/ncomms2043.
[4]BARZ S,KASHEFI E,BROADBENT A,et al.Demonstration of blind quantum computing[J].Science,2011,335(6066):303.DOI:10.1126/science.1214707.
[5]BREZULEANU A.Delegating private quantum computations[J].Canadian Journal of Physics,2015,93(9):941-946.DOI:10.1139/cjp-2015-0030.
[6]AHARONOV D,BEN-OR M,EBAN E.Interactive Proofs for Quantum Computations[DB/OL].[2018-06-04].https://www.researchgate.net/publication/221463088_Interactive_Proofs_For_Quantum_Computations.
[7]REICHARDT B W,UNGER F,VAZIRANI U.Classical command of quantum systems[J].Nature,2013,496(7446):456-460.DOI:10.1038/nature12035.
[8]FITZSIMONS J F,KASHEFI E.Unconditionally verifiable blind quantum computation[J].Physical Review A,2017,96:012303.DOI:10.1103/PhysRevA.96.012303.
[9]MORIMAE T.Verification for measurement-only blind quantum computing[J].Physical Review A,2014,89(6):4085-4088.DOI:10.1103/PhysRevA.89.060302.
[10]HAYASHI M,MORIMAE T.Verifiable measurementonly blind quantum computing with stabilizer testing[J].Physical Review Letters,2015,115(22):220502.DOI:10.1103/PhysRevLett.115.220502.
[11]DEUTSCH D,JOZSA R.Rapid Solution of Problems by Quantum Computation[R].Bristol:University of Bristol,1992.
[12]SHOR P W.Algorithms for quantum computation:Discrete logarithms and factoring[C]//Symposium on Foundations of Computer Science.Washington D C:IEEEComputer Society,1994:124-134.DOI:10.1109/SFCS.1994.365700.
[13]HILLERY M,BUZEK V,BERTHIAUME A.Quantum secret sharing[J].Physical Review A,1999,59(3):1829-1834.
[14]BAI C M,LI Z H,XU T T,et al.A generalized information theoretical model for quantum secret sharing[J].International Journal of Theoretical Physics,2016,55(11):4972-4986.DOI:10.1007/s1 0773-016-3121-9.
[15]DENG F G,GUI L L,ZHOU H Y.An efficient quantum secret sharing scheme with Einstei-Podolsk-Rosen pairs[J].Physics Letters A,2006,340(1):43-50.DOI:10.1016/j.physleta.2005.04.007.
[16]BAI C M,LI Z H,LIU C J,et al.Quantum secret sharing using orthogonal multiqudit entangled states[J].Quantum Information Processing,2017,16(12):304.DOI:10.1007/s11128-017-1739-z.
[17]XIAO L,LONG G L,DENG F G,et al.Efficient multiparty quantum-secret-sharing schemes[J].Physics,2004,69(5):521-524.DOI:10.1103/PhysRevA.69.052307.
[18]XU T T,LI Z H,BAI C M,et al.A new improving quantum secret sharing scheme[J].International Journal of Theoretical Physics,2017,56:1-10.DOI:10.1007/s10773-016-3272-8.
[19]TITTEL W,ZBINDEN H,GISIN N.Experimental demonstration of quantum secret sharing[J].Physical Review A,2001,63(4):42301.DOI:10.1103/PhysRevA.63.042301.
[20]BAI C M,LI Z H,XU T T,et al.Quantum secret sharing using the d-dimensional GHZ state[J].Quantum Information Processing,2017,16(3):59.DOI:10.1007/s11128-016-1506-6.
[21]BAI H Y,LI Z H,HAO N.Quantum Security Computation on Shared Secrets[DB/OL].[2018-05-12].https://arxiv.org/pdf/1804.03792.pdf.DOI:10.1007/s10773-018-3905-1.
[22]HILLERY M,BUZEK V,BERTHIAUME A.Quantum secret sharing[J].Physical Review A,1999,59(3):1829-1834.
[23]CLEVE R,GOTTESMAN D,LO H K.How to share a quantum secret[J].Physical Review Letters,1999,83(3):648-651.DOI:10.1103/PhysRevLett.83.648.
[24]GOTTESMAN D.Theory of quantum secret sharing[J].Physical Review A,2000,61(4):192-193.DOI:10.1103/Phys-RevA.61.042311.
[25]ZHANG Z J,MAN Z X.Multiparty quantum secret sharing of classical messages based on entanglement swapping[J].Physical Review A,2005,72(3):15-19.DOI:10.1103/PhysRevA.72.022303.
[26]MARKHAM D,SANDER B C.Graph states for quantum secret sharing[J].Physical Review A,2008,78(4):042309.DOI:10.1103/PhysRevA.78.042309.
[27]DEUTSCH D,BARENCO A,EKERT A.Universality in quantum computation[J].Proceedings Mathematical&Physical Sciences,1995,449(1937):669-677.
[28]ZHOU X,LEUNG D W,CHUANG I L.Methodology for quantum logic gate constructions[J].Physical Review A,2000,62(5):052316.DOI:10.1103/Phys RevA.62.052316.
[29]OUYANG Y,TAN S H,ZHAO L,et al.Computing on quantum shared secrets[DB/OL].[2018-06-04].https://journals.aps.org/pra/pdf/10.1103/PhysRevA.96.052333.