本講主要內(nèi)容1糾纏態(tài)知識回顧2Ekert

91協(xié)

議3基于糾纏的BB84協(xié)議4

MDI-QKD協(xié)議5

TF-QKD協(xié)議1糾纏定義，檢測21糾纏態(tài)知識回顧糾纏態(tài)的定義■

不可分離態(tài)不可分離態(tài)，即糾纏態(tài)，指不能寫成可分離態(tài)形式的態(tài)，即兩體系統(tǒng)的態(tài)不能簡單地寫成兩個子系統(tǒng)態(tài)的直積形式|φ>

A?|φ>B。糾纏態(tài)包括糾纏純態(tài)和糾纏混態(tài)。Bell態(tài)是最簡單的兩體量子糾纏態(tài)，在測量前A和

B處于不確定的狀態(tài)，若對其中之

一進行測量，則另一個的狀態(tài)隨之而定，即塌縮到確定態(tài)。兩體糾纏態(tài)Bell

態(tài)，共有4個3多粒子糾纏GHZ-stateGraph-statecluster-stateW-state4θ?=θ。對應(yīng)“90/0度”測量基，

θ?=θ/對應(yīng)“-45/45度”測量基若發(fā)送最大糾纏態(tài)，如

Bell態(tài)

4

〉A(chǔ)后，則S=2√2;對于非糾纏態(tài)，|S|≤2。Bell

參數(shù)：S=E(θ,On/s)-E(0,O?π/8)+E(O2/4,D/8,)+E(O2/4,03π/8)相關(guān)系數(shù)糾纏態(tài)的檢驗：CHSH

不等式其中，

θB=03π/18對應(yīng)“67.51-22.5度”測量基，

θB=θ2/18兩光子偏振糾纏態(tài)可表示為：對應(yīng)“22.5/-67.5度”測量基，Alice的測量軸

Bob的測量軸52

Ekert

91協(xié)

議■協(xié)議原理、過程與實現(xiàn)■

密鑰產(chǎn)生率

(Key

rate)6基于E-91協(xié)議的QKD系統(tǒng)構(gòu)成裝

置(

Alice)PBS糾纏源2(90)5(45)3(22.5)

1(0)6(-45)4(-67.5)裝

置(Alice)b:1,2’

b?:3',4′5’5'(67.5)3’(45)1'(22.5)6'(-22.5)4'(-45)2'(-67.5)后處理1’BobPBSBS

1:26'PBSHWP?I3'PBSHWP?PBS后處理Alice測量同步測量同

步2’HWP?1:1

BSHWP?BS?

1:2E-91協(xié)議-過程E91

協(xié)議的工作過程如下：?Step1.糾纏源產(chǎn)生糾纏光子對,每對糾纏光子對中的兩個光

子分別發(fā)往

A

和

B;?Step2.A

和

B各自對每組光子進行獨立測量，其中測量基矢從三組特定基矢中隨機選取

，A從測量基(a:a?,a?)

中隨機選取，B從測量基(b,b?

,b?)中隨機選取；Step3.經(jīng)過多次測量后，雙方通過經(jīng)典信道公布各自所選用的測量基，并將測量得

到的隨機數(shù)分為兩部分：測量基相同(a?

與

b;a?與

b?)的部分將各自繼續(xù)持有，而測

量基不同的部分則通過經(jīng)典信道告之對方；

?8E-91協(xié)議-過程(續(xù))Step4.

利用測量基不同的部分進行竊聽檢測，即計算

Bell

參數(shù)，檢測CHSH

不等式

：?S=E(a,b)-E(a,b?)+E(as,b?)+E(a,b?)其中,

E(a.b?)=P.(ab,)+P.(ab?)-P.(a.b?)-P.(ab?)P.

(a,b,)表示A沿a基測量，B沿b,基測量，測量結(jié)果都為+1的概率，其它的類同。Step5.如判定無竊聽者存在，即|s|>2,

由于雙方的測量結(jié)果具有反關(guān)聯(lián)性(如Alice得到的結(jié)果是0,Bob

得到的結(jié)果必定是1),對其中之一做比特反轉(zhuǎn)，即得到初

始密鑰(initial

key,也稱為篩選密鑰，sifted

key);?Step6.

執(zhí)行信息協(xié)調(diào)和密性放大，得到最終安全密鑰。?9E-91協(xié)議-Key

rate■

密鑰產(chǎn)生率RE?1≥qQ[1-f(e)H?(e)-x(B:E)]10E-91協(xié)議Keyrate結(jié)果tB≠1時106Onm波長暗計數(shù)10-1310?(d)波長1060nm

時

E91協(xié)議密鑰率.與損耗關(guān)系圖(tg≠1

且暗計數(shù)10-13).20

2122鏈路損耗

(dB)2325密鑰率113基于糾纏的BB84協(xié)議■

糾纏制備■分別隨機選擇測量基

(Z\X)12BBM92

協(xié)議BBM92協(xié)議的具體工作過程如下：Step1.糾纏源產(chǎn)生處于Bell態(tài)的糾纏光子對，糾纏光子對中的兩個光子分別發(fā)往

A

和B;?Step2.A

和B

各自對收到的每組光子進行獨立測量，A和

B

的測量基矢分別從Z基(0/90)或X基(45/-45)中隨機選??；

?Step3.經(jīng)過多次測量后，雙方公布各自所選用的測量基，并將收到的隨機數(shù)分為兩部分：測量基相同的部分各自保留，而測量基不同的部分丟棄，得到初始密鑰；

?Step4.A

和B從初始密鑰中隨機選擇部分比特公開比較進行竊聽檢測，誤碼率小于門限值的情況下，進行下一步；否則認為存在竊聽，終止協(xié)議；

?Step5.如判定無竊聽者存在，執(zhí)行信息協(xié)調(diào)和密性放大，得到最終安全密鑰。

?13基于糾纏的BB84協(xié)議實現(xiàn)Alice:Detection

ModuleA.Poppe,A.Fedrizzi,T.Loruenser,O.Maurhardt,R.Ursin,H.R.Boehm,M.Peev,M.Suda,C.Kurtsiefer,H.Weinfurter,T.Jennewein,A.Zeilinger.PracticalQuantumKeyDistributionwithPolarization-EntangledPhotons.Optics

Expression,2004,vol.12,No.16:3856HWPSvnc.LaserlEthernetPo.n:SMFODBBOHWPQKGElectronicsQKGElectronicsEth

Bidge-Ethernet

PortEthemet

Port1.45

kmclentEthernetBBO/2SMF144

MDI-QKD協(xié)議15測量設(shè)備無關(guān)量子密鑰分發(fā)■

MDI-QKD(measurement

device

independent

quantumkeydistribution)Lo

HK,Curty

Mand

Qi

B

2012

Phys.Rev.Lett.10813050316MeasurementdeviceBSDecoy-IMPol-MWCPAliceDecoy-IMPol-MWCPBobD?

HPBSD?vDHPBSD?VTransmissioncoefficient

T=cos2θReflectioncoefficientR=1-T=sin2θ

Relativephase

ie±iMappingofoperatorsa?=cos

θa+ie-i

sin

θa?a?=iei

sin

θa+cos

θaora→iei

sinθa3+cosθa?a?→cos

θas+ie?i

sin

θa?P.

Kok,W.J.Munro,K.Nemoto,T.C.Ralph,J.P.Dowling,G.J.Milburn,Linear

optical

quantum

computing

with

photonicqubits,Rev.Mod.Phys.79135(2007)17Fora

50:50

BSθ=π/4φ=0

分束器

Beam

splitter(BS)31218H.-K.Lo,M.Curty,B.Qi,Measurement-Device-Independentquantumkey

distribution,PhysicalReviewLetters,108130503(2012)Bellstatemeasurement(BSM4〉?B=(a?|H>a+av|V>)(Ba|H〉。+BIV>)=αHβH|H〉

|H〉B+αHB|H>|V〉B+avβH|V>|H〉B+αvβ|V>AIV>B4〉A(chǔ)=aH|H〉A(chǔ)+av|V〉=(ana?.A+ava.,A)|0)4〉B=βa|H〉?+B|V〉B=(Baaa.B+Bva.B)|0)0〉A(chǔ)|So,we

can

identify

4+>AB

the

by

coincidence

betweenD?H

and

D?v

or

in

D?H

and

D?v19[a,a.]=δ(k-K'),[a,ae]=[a,a

徒]=0Commutation

relation

is

used.BSM(cont.)So,thereisnocoincidencebetweenfourdetectorsforinputstates|φ〉A(chǔ)DABSo,we

can

identifyl4

?B

the

by

coincidence

betweenD?w

and

D?H

or

in

D?n

and

D?vαH=βH,αv=βv

,the

transformation

will

be〉?

4〉B=(anaaA+avatA)(Baa

B+Bva

B)

0〉BSM(cont.)-If4

|

..

.

.|Hong-Ou-Mandel

effectBSM(cont.)AtMDI-QKDAlice

&BobRelayoutput|

ψ〉Relay

output

|

ψ+〉Rectilinearbasis

Diagonal

basisBitflipBit

flipBitflipNobit

flipH.-K.Lo,M.Curty,B.Qi,Measurement-Device-Independent

quantum

key

distribution,Physical

Review

Letters,108130503(2012)ABMDI-QKD實現(xiàn)Liu

Y,Chen

TY,Wang

LJet

al

2013

Phys.Rev.Lett.11113050222USERNLaser

AM

Circ

PM

EVOA

DWDM

EPC

PBS

SNSPD普通的QKD網(wǎng)絡(luò)與MDI-QKD網(wǎng)絡(luò)

MDI-QKD

網(wǎng)絡(luò)：一個測量服務(wù)器，三個用戶Tang

YL,Yin

HL,Zhao

Qet

al

2016

Phys.Rev.X6011024MDI-QKD網(wǎng)絡(luò)(a)USERN(b)OpticalSwitchOptical

SwitchAttack!USER2USER223BSfD?IIBS?△t=tVIVBS,AliceCharlieSPSTime-binMeasurementsetupTime-binencoderSPSDavid基

于W

態(tài)

的

四

用

戶MDI-QKD

網(wǎng)

絡(luò)

W態(tài)分析器[1]ChanghuaZhu,FeihuXu,Changxing

Pei,W-state

Anabyzer

and

Multi-party

Measurement-device-independent

QuantumKeyDistribution,ScientificReports,5,17449(2015)4用戶MDI-QKD

網(wǎng)絡(luò)Time-bin

encoderSPSBobI△t=T△t=Tw

BS??u

BS,Time-bin

encoderBS?△t=TBS?BS?BS?BSSPSCgIID?D?D?BS?ADB24mhbkC5

TF-QKD協(xié)議25PMM.Lucamarini,Z.L.Yuan,J.F.Dynes1&A.J.Shields,Overcomingtherate-distancelimitof

quantum

key

distribution

without

quantum

repeaters,Nature557,400(2018)TF-QKD

原理BobLSMbIMCharlieDO

D1LSIMPMVOAAliceVOARNGRNG26M.Lucamarini,Z.L.Yuan,J.F.Dynes1&A.J.Shields,Overcoming

the

rate-distance

limit

of

quantum

key

distribution

without

quantum

repeaters,Nature

557,400(2018)Typical

phase-basedQKD

set-upUnfoldedQKD

set-upTF-QKD原理(續(xù))27Protocol0.Initial

operations-The

phase

interval(0,2π)is

split

into

M=16equal

slices

△c=2πk/M,withk={0,.…..M-1}.An

authenticated

channel

is

set

up

for

the

public

announcements

made

by

the

legitimateusers

Alice

and

Bob.1.Classical

stage-The

users

send

bright

unmodulated

optical

pulses

to

the

relay

station,to

let

Charliestabilise

the

communication

channels

and

in

particular

minimise

the

phase

misalignment

δba=δ-8a.2.Quantum

stage-The

users

attenuate

the

optical

pulses

to

the

single-photon

level

and

modulatetheir

phase

and

intensity.3.Preparation-Alice

and

Bob

select

random

values

for

the

intensities

Ha,b∈{u/2,v/2,w/2};the

bitphasesαa,b∈{0,π},corresponding

to

the

bits{0,1},respectively;the

basis

phasesβa,b∈{0,π/2},

corresponding

to

the

bases{X,Y},respectively;and

the

phases

Pa,b∈(0,2π).They

record

in

whichphase

slice

△k(a)(Alice)or

△e(b)(Bob)their

values

pa

and

pb

fall

into.They

then

prepare

pulseswithintensitiesμa,b

andphases

φa,b=(aa,b+βa,b+Pa,b)田2πandsend

them

toCharlie.M.Lucamarini,Z.L.Yuan,J.F.Dynes1&A.J.Shields,Overcoming

the

rate-distance

limitof

quantum

key

distribution

without

quantum

repeaters,Nature

557,400(2018)TF-QKDprotocol284.Charlie's

measurement

and

announcement-Charlie

interferes

the

incomingpulses

and

records

which

detector

clicks.When

the

quantum

communication

is

over,he

publicly

announces

all

the

runs

where

his

detector

0(1)clicked;Alice

and

Bob

will

correspondingly

set

a

variable

x

equal

to

0(π).All

theruns

where

none

oforboth

ofhis

detectors

clicked

are

discarded.5.

Users'sannouncementand

sifting-Afterthe

previous

stepiscomplete,Aliceannouncestheintensi-

ties

μa,the

basis

phases

βa

and

the

phase

slices

△k(a)and

Bob

announces

the

runs

where

his

valuesmatch

Alice's.The

users

discard

all

the

mismatched

runs.Then

they

disclose

the

bit

values

of

the

matched

runs

except

those

in

basis

X

and

intensity

class

u,which

are

kept

secret.6.Raw

key

bit

distillation

and

parameter

estimation-The

users

perform

a

coordinated

random

per-

mutation

of

the

bits.For

the

bits

in

basis

X

and

intensity

class

u,Bob

draws

Alice's

bit

phase

αafrom

the

relation

x=|ab-αa|.The

userscanthendistillakey

bitequalto0(1)whenαa=0

(π).A

raw

key

is

formed

by

concatenating

these

bits.All

the

remaining

bits,fully

disclosed

in

theprevious

step,are

used

to

perform

the

decoy-state

parameter

estimation

and

test

the

channel

againstthe

presence

ofEve.7.Post-processing-Theusersrun

classical

post-processing

proceduressuchas

error

correction

and

privacy

amplification

to

distil

the

final

secure

key

from

theraw

key.Table

S1-TF-QKDprotocol.M.Lucamarini,Z.L.Yuan,J.F.Dynes1&A.J.Shields,Overcomingtherate-distancelimitof

quantumkeydistributionwithoutquantumrepeaters,Nature557,400(2018)TF-QKDprotocol29TF-QKD

協(xié)議TF-QKD

協(xié)議的工作過程如下：(1)制備：Alice

產(chǎn)生隨機信息比特序列8a,隨機選擇從{X,Y}中選擇編碼基進行相位編碼，{X,Y}

基分別對應(yīng)h∈{0,1},同時借助相位調(diào)制器

PM

進行相位隨機化，隨機相位為

θa,θa∈[0,2π],則制備的量子態(tài)為

同

理

，Bob

制

備

的

量

子

態(tài)(2)測量：Alice

和

Bob

將編碼后的量子態(tài)發(fā)送給Charlie,

在

Charlie

的分束器

(BS)處進行

單光子干涉，再根據(jù)探測器D?和D?

的響應(yīng)來確定Bell態(tài)測量結(jié)果；X:

0,π30TF-QKD協(xié)議(續(xù))(3)篩選：Charlie

通過Alice

和

Bob

雙方共同認證的經(jīng)典信道公開測量結(jié)果，Alice和

Bob

公開各自的h,θa和h,θ?。其中，對于Alice和

Bob的隨機相位信息θa,θ,雙方無需公布具體的相位值，只需公布各自所在的相位區(qū)間信息△R(a,b)即可(這里，將可能的相位取值[0,2π)分成

M

個相位區(qū)間，即△=2πk/M,k={0,K,M-1}

。

如果

Charlie

的探測器D?,D?

有且僅有一個響應(yīng)，并且

Alice和

Bob的隨機相位落在同一個區(qū)間內(nèi)，則Alice和Bob保留各自的信息比特ga,gb,

其余全部丟棄。Alice

和

Bob

利用部分原始數(shù)據(jù)計算QBER,

若該值小于預(yù)設(shè)的閾值，則剩余比特成為初始密鑰，否則，此次密鑰傳輸無效，丟棄全部數(shù)據(jù)。(4)后處理：Alice和

Bob對篩選后的初始密鑰進一步糾錯和密性放大，以防存在竊聽者

Eve竊取信息，得到最終安全密鑰。311010.Simulationparameters(Hz)(%)108-ldeal

bounds

0

100

0TF-QKD

1030

3

1.1510?-13IdealTF--cQKD

Single-repeaterbound□6TF-QKDRepeaterlessboundsbit

h-110-4-0100

200300

400500

600

Alice-Bobdistance

in

standard

opticalfibre

(km)Theoreticalbounds(lines)andexperimentalresults(symbol