info[x_]  :=  -x Log[2, x]h[x_]  :=  info[x]  +  info[1 - x]ph[n_, l_, e_]  :=  
      Exp[-n 
          l^2 /(2 e ( 1 -  e) ((1 +  l/2  e)^2))]pm[n_, d_,  g_, e_]  :=   
      2^(n (h[g e]  -  h[e]  +  d))

BobInfo[n_, b_, d_, e_] := 
  Max[0, (1 - 2*Exp[-(n*b^2)])]*Max[0,(1 - (Sqrt[2*n]*2^(1 - n*(d + h[e - b] - h[e])))/Log[2])]

alpha[n_,  b_,  d_,  e_]  :=  1 -  BobInfo[n, b, d, e]

temp1[n_, b_, d_, e_] := 
      (1  -  
          (Sqrt[2*n]*2^
                  (1  -  n*(d  +  h[e  -  b]  -  h[e])))/
            Log[2])temp2[n_, b_, d_, e_] := (1  -  2*Exp[-(n*b^2)])

temp4[n_, g_, e_]  :=  
      1 - ((1 - ph[n, g e (1/2  -  e)/2,  e])^2) 
          (1  -  pm[n,  (h[e]  -  h[g e])/2,  g,  e])

Plot3D[temp4[300,  g,  e], {g, 0, 1},  {e, 0, 1/2}]

FindMinimum[ temp4[3000, g, 0.01], {g,  {0.01, 1}}]

Plot[ 
      Replace[g, 
        (FindMinimum[ temp4[30000, g, e], {g,  {0.01, 1}},  
              WorkingPrecision  ->  30])[[2]]], 
       {e,  0.010000,  0.400000}]

Plot[{temp1[1000, b,  0.08,  0.4], temp2[1000,  b, 0.08, 0.4]}, {b, 
        0, 0.085}]

Plot3D[alpha[1000, b, d, 0.4], {b, 0, 0.1}, {d, 0, 0.08}]

//  
      We assume that the first factor in Bob' s info isn' t 
        important

BobInfo2[n_, g_, e_]  :=  
      1  -  (Sqrt[2*n]*2^(1  -  n*( h[e]  -  h[g e])/2))/
          Log[2]

BobInfo2[350, 0.8,  0.4]

Plot3D[ BobInfo2[350,  g,  e], 
       {g,  0.4, 0.9999}, {e, 0.0001, 0.5}]

Plot[ BobInfo2[300,  0.9,  e],  {e, 0.1, 0.4}]