#OK to post homework
#Nick Belov, Feb 16nd 2025, Assignment 8
read "C8.txt";

#1
for i from 1 to 3 do
    M := RHM(3,10):
    V := RSV(3,10):

    expVal1 := evalf(ProbDist(M,V)[3]):
    expVal2 := evalf(ExpMV(M,V)):

    print(expVal1,expVal2);
od:
print("-------------------------------");

#2 
for t from 1 to 3 do
    V := RSV(2,100):
    M := PM():
    s := evalf( ExpMV(M[1], V)^2 + ExpMV(M[2], V)^2 + ExpMV(M[3], V)^2 );
    print(s);
od:

#3
EntanglementAlice := proc(V)
    local M, sum, i;
    M := PM();
    sum := 0;
    for i from 1 to 3 do
        sum := sum + (ExpMV(TP(M[i], M[4]), V))^2;
    od;
    return sum;
end:
EntanglementBob := proc(V)
    local M, sum, i;
    M := PM();
    sum := 0;
    for i from 1 to 3 do
        sum := sum + (ExpMV(TP(M[4], M[i]), V))^2;
    od;
    return sum;
end:

RandomProductState4 := proc(K)
local a, b, productMatrix, productState;
    a := RSV(2, K):
    b := RSV(2, K):
    productMatrix := TP([a], [b]):    
    productState := productMatrix[1]:
    return productState;
end:

minAlice := 1e10: 
maxAlice := -1e10:
minAliceV := NULL: 
maxAliceV := NULL:
minBob   := 1e10: 
maxBob   := -1e10:
minBobV   := NULL: 
maxBobV   := NULL:

for j from 1 to 20 do
    V := RSV(4,10):
    EA := evalf(EntanglementAlice(V)):
    EB := evalf(EntanglementBob(V)):
    if EA < minAlice then
       minAlice := EA: 
       minAliceV := V:
    fi:
    if EA > maxAlice then
       maxAlice := EA: 
       maxAliceV := V:
    fi:
    
    if EB < minBob then
        minBob := EB: 
        minBobV := V:
    fi:
    if EB > maxBob then
        maxBob := EB:
        maxBobV := V:
    fi:
od:

print("Results over 20 random RSV(4,10) vectors:"):
print(minAlice):
print(minAliceV):

print("For EntanglementBob:"):
print(minBob):
print(minBobV):