Datasets:
wesley7137
/
quantum

Dataset card Data Studio Files
xet
 Community
text
stringlengths
0
8.13M
Let V and V be the set of qubits in the red
1 2 1. If p 1 ǫ and p <1 ǫ, then
Gpass ψpass
dotted box and the blue dotted box in Fig. 1, ≥ − −
respectively. Alice stores qubits in V 2 in her px∈/L < q+ 1 −q + 1 −q (1 ǫ) β .
memory, and measures each qubit in V in Z acc 2 2 − ≡ 1
1
4
2. If p <1 ǫ and p 1 ǫ, then which means
Gpass ψpass
− ≥ −
px ac∈/ cL < q+ 1 − q (1 −ǫ)+ 1 − q =β 1. (cid:12)Tr(Πρ) −Tr(ΠG Ψ′) (cid:12)≤δ
2 2
(cid:12) (cid:12)
for the POVM element Π corresponding to the accep-
3. If p Gpass <1 ǫ and p ψpass <1 ǫ, then tance of the measurement-based quantum computing.
− −
Therefore, the total acceptance probability, px∈/L, is
1 q 1 q acc
px∈/L < q+ − (1 ǫ)+ − (1 ǫ)
acc 2 − 2 − 1 q 1 q
px∈/L q(b+δ)+ − + −
= q+(1 q)(1 ǫ) β 2. acc ≤ 2 2
− − ≡
= q(b+δ)+(1 q) β .
3
− ≡
Letus considerthe remainingcase, p 1 ǫ and
Gpass
≥ −
p ψpass 1 ǫ. From the triangle inequality and the Let us define
≥ −
invariance of the trace norm under a unitary operation,
we obtain ǫ(1 q)
∆ (q) α β =q(a 1)+ − ,
1 1
≡ − − 2
1 1
2 ρ −G Ψ′ 1 = 2 ρ −G σ+G σ −G Ψ′ 1 ∆ 2(q) ≡ α −β 2 =q(a −1)+ǫ(1 −q),
(cid:13) (cid:13) (cid:13) (cid:13) ∆ (q) α β =q(a b δ).
(cid:13) (cid:13) 1(cid:13) 1 (cid:13) 3 ≡ − 3 − −
≤ 2 ρ −G σ 1+ 2 G σ −G Ψ′ 1 The optimal value
(cid:13) (cid:13) (cid:13) (cid:13)
= 1(cid:13) ρ G (cid:13) + 1(cid:13) σ Ψ′ Ψ(cid:13) ′ , ǫ
2 − σ 1 2 −| ih | 1 q∗ 2
(cid:13) (cid:13) (cid:13) (cid:13) ≡ 1+ ǫ b δ
(cid:13) (cid:13) (cid:13) (cid:13) 2 − −
where G Ψ′ G Ψ′ G Ψ′ ,
≡| ih |
of q is that satisfies ∆ (q) = ∆ (q). Then, if we take
1 3
G CZ (σ G G) CZ , a=1 2−r and b=2−r for a polynomial r,
σ ≡ e ⊗| ih | e −
(cid:0)e∈EO (cid:1) (cid:0)e∈EO (cid:1)
connect connect ǫ(a b δ)
∆ (q∗) = 2 − −
and σ is any 3m-qubit state on V 2. Since p Gpass 1 ǫ, 3 1+ ǫ b δ
the first term is upperbounded as ≥ − 2 − −
ǫ 2
1 2−r+1 2√2ǫ +ǫ
1 ρ G √2ǫ, ≥ 4 (cid:16) − − −r3 (cid:17)
2 − σ 1 ≤ 1
(cid:13) (cid:13) .
(cid:13) (cid:13) ≥ poly(x)
from Eq. (1). We can show that if p ψpass 1 ǫ, the | |
≥ −
second term is upperbounded as
As usual, the inverse polynomial gap can be amplified
with a polynomial overhead.
1 2
σ Ψ′ Ψ′ √2ǫ+ +ǫ. (3)
2 −| ih | 1 ≤ r3
(cid:13) (cid:13)
(cid:13) (cid:13)
The proof is given in Appendix. Acknowledgments
Therefore, we obtain
TM is supported by the Grant-in-Aid for Scientific
1 ρ −G Ψ′ 2√2ǫ+ r2 +ǫ R Jae ps aea nr ,ch ano dn thIn en Gov ra at niv t-e inA -Are idas foN ro. Y1 o5 uH n0 g08 S5 c0 ieo nf tisM tsE (X BT
2 1 ≤ 3 )
(cid:13) (cid:13)
(cid:13) (cid:13) δ, No.26730003of JSPS.
≡
[1] R. Raussendorf and H. J. Briegel, A one-way quantum (2012).
computer. Phys.Rev.Lett. 86, 5188 (2001). [5] T.Morimae,Continuous-variableblindquantumcompu-
[2] R. Raussendorf, D. E. Browne, and H. J. Briegel, tation. Phys.Rev. Lett.109, 230502 (2012).
Measurement-based quantum computation on cluster [6] V.Dunjko,E.Kashefi,andA.Leverrier,Universalblind
states. Phys. Rev.A 68, 022312 (2003). quantum computing with weak coherent pulses. Phys.
[3] A. Broadbent, J. F. Fitzsimons, and E. Kashefi, Uni- Rev. Lett.108, 200502 (2012).
versal blind quantum computation. 50th Annual IEEE [7] V. Giovannetti, L. Maccone, T. Morimae, and T. G.
SymposiumonFoundationsofComputerScience(2009). Rudolph,Efficientuniversalblindquantumcomputation.
[4] T.MorimaeandK.Fujii,Blindtopologicalmeasurement- Phys. Rev.Lett. 111, 230501 (2013).
based quantum computation. Nat. Comm. 3, 1036 [8] A. Mantri, C. A. Perez-Delgado, and J. F. Fitzsimons,
5
Optimal blind quantum computation. Phys. Rev. Lett. Device-independent verifiable blind quantum computa-
111, 230502 (2013). tion. arXiv:1502.02563
[9] T. Morimae and K. Fujii, Secure entanglement distilla- [20] S.Barz,J.F.Fitzsimons,E.Kashefi,andP.Walther,Ex-
tionfordouble-serverblindquantumcomputation.Phys. perimental verification of quantum computations. Nat.
Rev.Lett. 111, 020502 (2013). Phys. 9, 727 (2013).
[10] V. Dunjko,J. F. Fitzsimons, C. Portmann, and R.Ren- [21] C. Greganti, M. C. Roehsner, S. Barz, T. Morimae, and
ner, Composable security of delegated quantum compu- P. Walther, Demonstration of measurement-only blind