Textbook on QKD

I have written a textbook on quantum key distribution!

This textbook introduces the non-specialist reader to the concepts of quantum key distribution and presents an overview of state-of-the-art quantum communication protocols and applications. It presents the necessary mathematical tools without assuming much background, making it accessible to readers without experience in quantum information theory.

You can get it here.

Errata:

  • Definition 2.1: Third property (positivity) should be (φ,φ) ≥ 0.
  • Figure 2.2: The boundaries for θ are 0 ≤ θ ≤ π.
  • Exercise 2.20: The sum in the spectral decomposition of ρ is over i, not over x.
  • Definition 2.25 and Theorem 2.26: The map Ɛ is defined as  Ɛ : B(HA) → B(HB).
  • Definitions 2.31 and 2.34: The measurements Mx and M are defined as Mx : HA → HB and M : HA → HB.
  • Equation (2.103): The right hand side is 1/Sqrt{2}.
  • Equation (3.9): This should be h2(λ p1 + (1 − λ) p2) ≥ λ h2(p1) + (1 + λ) h2(p2).
  • Equations (3.15) and (3.18): Probability distributions are missing their respective arguments, namely pX,Y(x,y) and pX(x).
  • Equation (3.19): The second term should have a positive sign.
  • Equation (3.31): The second term is H(X1|Y).
  • Exercise 4.2: The way the measurement results form the bit string b is as follows: If Bob obtains the result -1, then the i-th bit of b is bi = 1, and if he obtains +1, then bi = 0.
  • Equation (4.44): The superscript of the smooth min-entropy is ε‘, and the last term on the right hand side (the logarithm) is missing a factor 2.
  • Beneath Equation (A.3): If X and Y are independent, pY|X(y|x) = pY(y) for all y ∈ Y.
  • Equation (B.4): He2 = (1 1)T, He3 = (0 1)T.
  • First full sentence on page 224: The quantum code CSS(C1,C2) is defined to be the vector space spanned by { |x + C2> }xϵC1 .