Quantum secret sharing with continuous variable graph state

In this paper, we study several physically feasible quantum secret sharing (QSS) schemes using continuous variable graph state (CVGS). Their implementation protocols are given, and the estimation error formulae are derived. Then, we present a variety of results on the theory of QSS with CVGS. Any $$(k,n)$$(k,n) threshold protocol of the three specific schemes satisfying $$\frac{n}{2}<k\le n$$n2<k≤n, where $$n$$n denotes the total number of players and $$k$$k denotes the minimum number of players who can collaboratively access the secret, can be implemented by certain weighted CVGS. The quantum secret is absolutely confidential to any player group with number less than threshold. Besides, the effect of finite squeezing to these results is properly considered. In the end, the duality between two specific schemes is investigated.

[1]  S. Braunstein,et al.  Continuous-variable Gaussian analog of cluster states (5 pages) , 2006 .

[2]  Guihua Zeng,et al.  Universal teleportation via continuous-variable graph states , 2008 .

[3]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[4]  Barry C. Sanders,et al.  Continuous-variable quantum-state sharing via quantum disentanglement , 2004, quant-ph/0411191.

[5]  R. Cleve,et al.  HOW TO SHARE A QUANTUM SECRET , 1999, quant-ph/9901025.

[6]  Debbie W. Leung,et al.  Quantum data hiding , 2002, IEEE Trans. Inf. Theory.

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

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

[9]  C. H. Oh,et al.  Nonadditive quantum error-correcting code. , 2007, Physical review letters.

[10]  T. Ralph,et al.  Continuous variable quantum cryptography , 1999, quant-ph/9907073.

[11]  Tomoyuki Morimae.  Continuous-variable blind quantum computation. , 2012, Physical review letters.

[12]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[13]  H. Kimble,et al.  Teleportation of continuous quantum variables , 1998, Technical Digest. Summaries of Papers Presented at the International Quantum Electronics Conference. Conference Edition. 1998 Technical Digest Series, Vol.7 (IEEE Cat. No.98CH36236).

[14]  P. Sarvepalli.  Nonthreshold quantum secret-sharing schemes in the graph-state formalism , 2012, 1202.3433.

[15]  W Dür,et al.  Multiparticle entanglement purification for graph states. , 2003, Physical review letters.

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

[17]  N. C. Menicucci,et al.  Quantum Computing with Continuous-Variable Clusters , 2009, 0903.3233.

[18]  Yu Wang,et al.  Toward demonstrating controlled-x operation based on continuous-variable four-partite cluster states and quantum teleporters , 2010, 1002.4272.

[19]  S. Braunstein,et al.  Continuous-variable Gaussian analog of cluster states , 2006 .

[20]  D. Markham,et al.  Quantum secret sharing with qudit graph states , 2010, 1004.4619.

[21]  G. Tóth,et al.  Bell inequalities for graph states. , 2004, Physical review letters.

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

[23]  Jing Zhang.  Graphical description of local Gaussian operations for continuous-variable weighted graph states , 2008 .

[24]  T. Ralph,et al.  Universal quantum computation with continuous-variable cluster states. , 2006, Physical review letters.

[25]  W. Bowen,et al.  Tripartite quantum state sharing. , 2003, Physical review letters.

[26]  L. Goddard.  Information Theory , 1962, Nature.

[27]  Seth Lloyd,et al.  Gaussian quantum information , 2011, 1110.3234.

[28]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[29]  Damian Markham,et al.  Equivalence between sharing quantum and classical secrets and error correction , 2012, 1205.4182.

[30]  曾贵华,et al.  The dependence of fidelity on the squeezing parameter in teleportation of the squeezed coherent states , 2011 .

[31]  J. Eisert,et al.  Multiparty entanglement in graph states , 2003, quant-ph/0307130.

[32]  Akira Furusawa,et al.  Demonstration of a reversible phase-insensitive optical amplifier , 2011, 1101.1139.

[33]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[34]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.