當量子位元從合法用戶傳輸時，Espian 無法從量子位元中獲取任何訊息，因為其中沒有編碼訊息。
只有在 Asja 和 Balvis 進行測量後，資訊才會「產生」。
然而，通常實現 E91 的方式是與設備獨立的方式，意思就是其中EPR 對的來源由第三方(Charlie) 控制，第三方生成糾纏量子位對並將一個量子位元發送給Asja，將第二個量子位元發送給Balvis。
如果 E91 作為設備獨立協議實現，Espian 可以使用中間人策略並在通往 Asja 和 Balvis 的途中攔截兩個量子位元！
他可以測量 EPR 對中的兩個量子位元並用假狀態替換它們（|00⟩或者|11⟩)
據我們所知，Asja 正在使用𝑍, 𝑋, 𝑊 bases (θ_A)， Balvis 使用𝑍, 𝑊, 𝑉 bases(θ_B)
取得密鑰位的回合為： 
和
剩餘回合用於測試 CHSH 不等式。
因此，Espian 只需要使用這些base！
所有用戶都會保存他們為每回合選擇的base的資訊。
# import all necessary objects and methods for quantum circuits
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, execute, Aer
from random import randrange
#Registers for measurement bases and keys
basesAsja, keyAsja = [],[]
basesBalvis, keyBalvis = [],[]
basesEspian, keyEspian = [],[]
for i in range(64): #Charlie prepares 64 EPR pairs
qreg = QuantumRegister(2)
creg = ClassicalRegister(2)
mycircuit = QuantumCircuit(qreg, creg)
#Creating entanglement
mycircuit.h(qreg[0])
mycircuit.cx(qreg[0], qreg[1])
#Espian intercepts qubits and chooses measurement basis
choiceEspian=randrange(2)
if choiceEspian==0:#measurement in Z basis
basesEspian.append('Z')
if choiceEspian==1:#measurement in W basis
mycircuit.s(qreg)
mycircuit.h(qreg)
mycircuit.t(qreg)
mycircuit.h(qreg)
basesEspian.append('W')
mycircuit.measure(qreg,creg) #applying final measurement
job = execute(mycircuit,Aer.get_backend('qasm_simulator'),shots=1)
counts = job.result().get_counts(mycircuit)
#Saving results
result=list(counts.keys())[0] #retrieve key from dictionary
keyEspian.append(int(result[0])) #saving first qubit value in Espian's key register
for i in keyEspian:#Espian preparing fake states
qregE = QuantumRegister(2)
cregE = ClassicalRegister(2)
mycircuitE = QuantumCircuit(qregE, cregE)
if keyEspian=='1': #if Espian obtained result 11 or 00, she will send corresponding states to Asja and Balvis
mycircuitE.x(qregE[0])
mycircuitE.x(qregE[1])
if keyEspian=='0':
pass #preparing state 00
#Asja chooses measurement basis
choiceAsja=randrange(3)
if choiceAsja==0:#measurement in Z basis
basesAsja.append('Z')
if choiceAsja==1:#measurement in X basis
mycircuitE.h(qregE[0])
basesAsja.append('X')
if choiceAsja==2:#measurement in W basis
mycircuitE.s(qregE[0])
mycircuitE.h(qregE[0])
mycircuitE.t(qregE[0])
mycircuitE.h(qregE[0])
basesAsja.append('W')
#Balvis chooses measurement basis
choiceBalvis=randrange(3)
if choiceBalvis==0:#measurement in Z basis
basesBalvis.append('Z')
if choiceBalvis==1:#measurement in W basis
mycircuitE.s(qregE[1])
mycircuitE.h(qregE[1])
mycircuitE.t(qregE[1])
mycircuitE.h(qregE[1])
basesBalvis.append('W')
if choiceBalvis==2:#measurement in V basis
mycircuitE.s(qregE[1])
mycircuitE.h(qregE[1])
mycircuitE.tdg(qregE[1])
mycircuitE.h(qregE[1])
basesBalvis.append('V')
mycircuitE.measure(qregE,cregE) #applying final measurement
job = execute(mycircuitE,Aer.get_backend('qasm_simulator'),shots=1)
countsE = job.result().get_counts(mycircuitE)
#Saving results
resultE=list(countsE.keys())[0] #retrieve key from dictionary
keyAsja.append(int(resultE[0])) #saving first qubit value in Asja's key register
keyBalvis.append(int(resultE[1])) #and second to Balvis
Asja 和 Balvis 使用經典通道比較base。他們將關鍵字串分為兩組——測量base匹配的組和base不匹配的組。它們儲存有關base的資訊並獲得base不匹配的回合的位元。
Espian傾聽他們的交流，並繼續他與Asja 和 Balvis相同的測量base的回合。
#Registers
finalKeyAsja, finalKeyBalvis = [],[] #for matching rounds
finalKeyEspian=[] #for matching rounds
diffAsja, diffBalvis = [],[] #missmatched rounds
diffBasesA, diffBasesB = [],[] #bases of missmatched rounds
#Users comparing rounds
for i in range(0, len(basesAsja)):
if basesAsja[i] == basesBalvis[i]: #When users used same bases
finalKeyAsja.append(keyAsja[i])
finalKeyBalvis.append(keyBalvis[i])
else: #When used different
diffAsja.append(keyAsja[i])
diffBalvis.append(keyBalvis[i])
diffBasesA.append(basesAsja[i])
diffBasesB.append(basesBalvis[i])
if (basesAsja[i] == basesEspian[i] and basesBalvis[i] == basesEspian[i]):
finalKeyEspian.append(keyEspian[i])
此時，我們可以知道Espianc獲得多少比例的密鑰
key_percent_Espian = (len(finalKeyAsja) - len(finalKeyEspian))/len(finalKeyAsja) # Espian's knowledge
print(key_percent_Espian)
0.5
#ZW
sameZW = 0
diffZW = 0
for i, (bA, bB) in enumerate(zip(diffBasesA, diffBasesB)):
if (bA == 'Z' and bB == 'W'):
if diffAsja[i]==diffBalvis[i]:
sameZW=sameZW+1
else:
diffZW=diffZW+1
totalZW=sameZW+diffZW
if totalZW!=0:
ZW=(sameZW-diffZW)/totalZW
else:
ZW=0
#XW
sameXW = 0
diffXW = 0
for i, (bA, bB) in enumerate(zip(diffBasesA, diffBasesB)):
if (bA == 'X' and bB == 'W'):
if diffAsja[i]==diffBalvis[i]:
sameXW=sameXW+1
else:
diffXW=diffXW+1
totalXW=sameXW+diffXW
if totalXW!=0:
XW=(sameXW-diffXW)/totalXW
else:
XW=0
#XV
sameXV = 0
diffXV = 0
for i, (bA, bB) in enumerate(zip(diffBasesA, diffBasesB)):
if (bA == 'X' and bB == 'V'):
if diffAsja[i]==diffBalvis[i]:
sameXV=sameXV+1
else:
diffXV=diffXV+1
totalXV=sameXV+diffXV
if totalXV!=0:
XV=(sameXV-diffXV)/totalXV
else:
XV=0
#ZV
sameZV = 0
diffZV = 0
for i, (bA, bB) in enumerate(zip(diffBasesA, diffBasesB)):
if (bA == 'Z' and bB == 'V'):
if diffAsja[i]==diffBalvis[i]:
sameZV=sameZV+1
else:
diffZV=diffZV+1
totalZV=sameZV+diffZV
if totalZV!=0:
ZV=(sameZV-diffZV)/totalZV
else:
ZV=0
S=ZW+XW-XV+ZV
print("CHSH inequality value is", S)
CHSH inequality value is 1.5595238095238093
由於Espian對金鑰分配過程的干擾，CHSH不等式值遠小於
透過這種方式，使用者可以確定他們的通訊是否受到損害，並且可以中止協議。
Espian可能會嘗試用自己準備的數據來誤導Asja和Balvis，但他不知道他們會選擇哪些測量基礎，因此行不通。
但現在會產生一個問題， Asja 和 Balvis 的最終密鑰不匹配！
print(finalKeyAsja)
print(finalKeyBalvis)
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
這種不匹配的原因是因為 Asja & Balvis 用𝑊𝑊進行測量。
Espian使用 |00⟩ 和 |11⟩作為假的量子狀態。
因此當 Asja 和 Balvis 用𝑊-base測量這些狀態時，他們會得到機率結果。
#Preparing state 00
qregT = QuantumRegister(2)
cregT = ClassicalRegister(2)
mycircuitTest = QuantumCircuit(qregT, cregT)
#Measuring in W-basis
mycircuitTest.s(qregT)
mycircuitTest.h(qregT)
mycircuitTest.t(qregT)
mycircuitTest.h(qregT)
mycircuitTest.measure(qregT,cregT)
job = execute(mycircuitTest,Aer.get_backend('qasm_simulator'),shots=100)
counts = job.result().get_counts(mycircuitTest)
print(counts) # counts is a dictionary
{'00': 67, '10': 15, '01': 14, '11': 4}
因此Asja & Balvis的量子位變成疊加態。
參考資料: womanium 教材
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