%PDF-1.4 % 4 0 obj (Introduction) endobj 5 0 obj << /D (section.2) /S /GoTo >> endobj 8 0 obj (Two kinds of quantum money) endobj 9 0 obj << /D (subsection.2.1) /S /GoTo >> endobj 12 0 obj (Quantum money with a classical secret) endobj 13 0 obj << /D (subsection.2.2) /S /GoTo >> endobj 16 0 obj (Collision-free quantum money) endobj 17 0 obj << /D (subsubsection.2.2.1) /S /GoTo >> endobj 20 0 obj (Quantum money by postselection) endobj 21 0 obj << /D (subsubsection.2.2.2) /S /GoTo >> endobj 24 0 obj (Verification using rapidly mixing Markov chains) endobj 25 0 obj << /D (subsection.2.3) /S /GoTo >> endobj 28 0 obj (An example of quantum money by postselection) endobj 29 0 obj << /D (subsubsection.2.3.1) /S /GoTo >> endobj 32 0 obj (Constructing a label function) endobj 33 0 obj << /D (subsubsection.2.3.2) /S /GoTo >> endobj 36 0 obj (Verifying the Quantum Money) endobj 37 0 obj << /D (subsubsection.2.3.3) /S /GoTo >> endobj 40 0 obj (A weakness of this quantum money) endobj 41 0 obj << /D (section.3) /S /GoTo >> endobj 44 0 obj (Insecurity of a previously published quantum money scheme) endobj 45 0 obj << /D (subsection.3.1) /S /GoTo >> endobj 48 0 obj (Attacking the verification circuit for 116m ) endobj 49 0 obj << /D (subsection.3.2) /S /GoTo >> endobj 52 0 obj (Recovering the classical secret for cm) endobj 53 0 obj << /D (section.4) /S /GoTo >> endobj 56 0 obj (Conclusions) endobj 57 0 obj << /D (section.5) /S /GoTo >> endobj 60 0 obj (Acknowledgments) endobj 61 0 obj << /D (section.5) /S /GoTo >> endobj 63 0 obj (References) endobj 64 0 obj << /D (appendix.A) /S /GoTo >> endobj 67 0 obj (Details of the attack against stabilizer money for 116m ) endobj 68 0 obj << /D (subsection.A.1) /S /GoTo >> endobj 71 0 obj (Procedure to Generate i) endobj 72 0 obj << /D (subsection.A.2) /S /GoTo >> endobj 75 0 obj (Review of the Phase Estimation Algorithm ) endobj 76 0 obj << /D (appendix.B) /S /GoTo >> endobj 79 0 obj (Insecurity of the Stabilizer Money for cm ) endobj 80 0 obj << /D (subsection.B.1) /S /GoTo >> endobj 83 0 obj (Properties of the Measurement Graph) endobj 84 0 obj << /D (subsection.B.2) /S /GoTo >> endobj 87 0 obj (Finding Planted Cliques in Random Graphs) endobj 88 0 obj << /D (subsection.B.3) /S /GoTo >> endobj 91 0 obj (Bounding 3,,m) endobj 92 0 obj << /D (subsection.B.4) /S /GoTo >> endobj 95 0 obj (Finding Cliques of Size cm) endobj 96 0 obj << /D [ 97 0 R /Fit ] /S /GoTo >> endobj 102 0 obj << /Filter /FlateDecode /Length 3484 >> stream xڽZY~_,E$uzdk{=>w QsIקRGY#AijHUu.ܽ_%.D&]A]Aa>|MhiNQ_E*dDygcL3O7nԋ_Fcm'E]>Z=n/CnOx] ӝ/#>vEyh>ʂDڢ <&ى09Y@QPLMsybߍC[]Xt _3ܟ%Nwgg$ Xh]mv*4K6lErLw_z'pB_FZZھ7qd?ƗYZE$]f!F3}_zS iɑ4Uc )$A`:`+s*2Pp!;>Qlf+?ڍEy?ɏu XVM4=< t췦7Z۸;3CYޟ=K⭮p4R, \qz4Ma/^o)eQO<m[cJM"I勈0lřd0g 5}PMwJqV !0q(3_.`5w[G %,c^k$_5xDִ{pU`A؞-PFA>y~t1|6i#fκߏUY| (^(;ϕ=5:F̹7 OwGK|7 =HK \XQYchm'*K_qtÅ'Q*ﴍ3H^b&ʏXj">DM .'}כb;o'qag!._1ʫJp_z^m|@ Ү;3?`zHgmZ˂3{bfd՟́| m2lM?q[Vnccw7.M~3۰@|q{g(;5ta,lW@5)ѩz1"-IġXk3'J>k:6 !:0/@{> .m?t{zlp,AL ,+"rNsXde(yb!wΗmvp0L%X 2q*^<@@AWmkdJScZ0lRa
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