A novel three-party quantum secret sharing scheme based on Bell state sequential measurements with application in quantum image sharing

In this work, we present a quantum secret sharing scheme based on Bell state entanglement and sequential projection measurements. The protocol verifies the $n$ out of $n$ scheme and supports the aborting of the protocol in case all the parties do not divulge in their valid measurement outcomes. The operator-qubit pair forms an integral part of the scheme determining the classical secret to be shared. The protocol is robust enough to neutralize any eavesdropping on a particular qubit of the dealer. The experimental demonstration of the scheme is done on IBM-QE cloud platform with backends \texttt{IBMQ\_16\_Melbourne} and \texttt{IBMQ\_QASM\_SIMULATOR\_V0.1.547} simulator. The security analysis performed on the scheme and the comparative analysis supports our claim of a stringent and an efficient scheme as compared to some recent quantum and semi-quantum techniques of secret sharing.

[1]  M. Kafatos.  Bell's theorem, quantum theory and conceptions of the universe , 1989 .

[2]  K. Boström,et al.  Deterministic secure direct communication using entanglement. , 2002, Physical review letters.

[3]  Sourya Joyee De,et al.  A Proposal for Quantum Rational Secret Sharing , 2015, ArXiv.

[4]  Guang-Can Guo,et al.  Quantum secret sharing without entanglement , 2002 .

[5]  Qin Li,et al.  Arbitrated quantum signature scheme using Bell states , 2009 .

[6]  Kai Lu,et al.  NEQR: a novel enhanced quantum representation of digital images , 2013, Quantum Information Processing.

[7]  Huawang Qin,et al.  Hierarchical Quantum Secret Sharing Based On Special High-Dimensional Entangled State , 2020, IEEE Journal of Selected Topics in Quantum Electronics.

[8]  Guihua Zeng,et al.  Arbitrated quantum-signature scheme , 2001, quant-ph/0109007.

[9]  N. Gisin,et al.  Experimental demonstration of quantum secret sharing , 2001 .

[10]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[11]  D. Markham,et al.  Graph states for quantum secret sharing , 2008, 0808.1532.

[12]  Huawang Qin,et al.  Verifiable (t, n) threshold quantum secret sharing using d-dimensional Bell state , 2016, Inf. Process. Lett..

[13]  Christian Kurtsiefer,et al.  Experimental single qubit quantum secret sharing. , 2005, Physical review letters.

[14]  L. Hsu.  Quantum secret-sharing protocol based on Grover's algorithm , 2003 .

[15]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[16]  Charles H. Bennett,et al.  Quantum cryptography using any two nonorthogonal states. , 1992, Physical review letters.

[17]  Z. Man,et al.  Multiparty quantum secret sharing of classical messages based on entanglement swapping , 2004, quant-ph/0406103.

[18]  Xiu-Li Song,et al.  (t, n) Threshold d-Level Quantum Secret Sharing , 2017, Scientific Reports.

[19]  Runhua Shi,et al.  Secret sharing based on quantum Fourier transform , 2013, Quantum Inf. Process..

[20]  Fuguo Deng,et al.  Improving the security of multiparty quantum secret sharing against Trojan horse attack , 2005, quant-ph/0506194.

[21]  Gilad Gour,et al.  Reducing the Quantum Communication Cost of Quantum Secret Sharing , 2011, IEEE Transactions on Information Theory.

[22]  Jian-Wei Pan,et al.  Efficient multiparty quantum-secret-sharing schemes , 2004, quant-ph/0405179.

[23]  Fuguo Deng,et al.  Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block , 2003, quant-ph/0308173.

[24]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[25]  D. Gottesman.  Theory of quantum secret sharing , 1999, quant-ph/9910067.

[26]  Huawang Qin,et al.  d-Dimensional quantum state sharing with adversary structure , 2015, Quantum Information Processing.

[27]  Barry C. Sanders,et al.  Erratum: Graph states for quantum secret sharing [Phys. Rev. A 78, 042309 (2008)] , 2011 .

[28]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[29]  Huawang Qin,et al.  Multi-dimensional quantum state sharing based on quantum Fourier transform , 2018, Quantum Inf. Process..

[30]  M. Dušek,et al.  Quantum identification system , 1998, quant-ph/9809024.

[31]  Jingliang Gao,et al.  Multi-party d-Level Quantum Secret Sharing Scheme , 2013 .

[32]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[33]  A. Zeilinger,et al.  Going Beyond Bell’s Theorem , 2007, 0712.0921.

[34]  M. Koashi,et al.  Quantum entanglement for secret sharing and secret splitting , 1999 .

[35]  Zhan-jun Zhang,et al.  Multiparty quantum secret sharing , 2004, quant-ph/0412203.

[36]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[37]  Hwayean Lee,et al.  Arbitrated quantum signature scheme with message recovery , 2004 .

[38]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[39]  Buzek,et al.  Quantum copying: Beyond the no-cloning theorem. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[40]  A. Holevo.  Bounds for the quantity of information transmitted by a quantum communication channel , 1973 .

[41]  Samaneh Mashhadi,et al.  General secret sharing based on quantum Fourier transform , 2019, Quantum Inf. Process..