By Sandor Imre, Laszlo Gyongyosi
Chapter 1 creation (pages 1–10):
Chapter 2 creation to Quantum info conception (pages 11–64):
Chapter three The Classical Capacities of Quantum Channels (pages 65–125):
Chapter four The Quantum skill of Quantum Channels (pages 126–155):
Chapter five Geometric Interpretation of Quantum Channels (pages 156–217):
Chapter 6 Additivity of Quantum Channel Capacities (pages 218–268):
Chapter 7 Superactivation of Quantum Channels (pages 269–324):
Chapter eight Quantum safeguard and privateness (pages 325–361):
Chapter nine Quantum conversation Networks (pages 362–387):
Chapter 10 fresh advancements and destiny instructions (pages 388–412):
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Additional resources for Advanced Quantum Communications: An Engineering Approach
The density matrix ρ of a simple pure quantum system which can be given in the state vector representation |ψ〉 = α|0〉 + β|1〉 can be expressed as the outer product of the ket and bra vectors, where bra is the transposed complex conjugate of ket, α hence for ψ = , ψ = [α * β * ] the density matrix is β 2 αβ * αα * αβ * α = β* ] = * . 3) The density matrix ρ = ∑ in=1 pi ψ i ψ i contains the probabilistic mixture of different pure states, representation of which is based on the fact that the mixed states can be decomposed into the weighted sum of pure states.
40) i =1 This density matrix is a diagonal matrix with the probabilities in the diagonal entries p1 0 ρ= 0 0 0 p2 0 0 0 . 42) l =1 where ∑ ln=1 pi = 1. 2 The Projective and POVM Measurement The projective measurement is also known as the von Neumann measurement and formally can be described by the Hermitian operator Z, which has the spectral decomposition Z= ∑λ P . 43) m where Pm is a projector to the eigenspace of Z with eigenvalue λm. 44) 22 CHAPTER 2 Introduction to Quantum Information Theory and they are pairwise orthogonal.
70) = , 2 2 where r′ = UrU† realizes a unitary transformation on r as a rotation (see Fig. 2). 71) where 0 ≤ γ ≤ 1, and ρ1 and ρ2 are pure states, and lie on a line segment connecting the density matrices in the Bloch sphere representation. Using probabilistic mixtures of the pure density matrices, any quantum state which lies between the two states can be expressed as a convex combination ρ = pρ1 + (1 − p ) ρ2 , 0 ≤ p ≤ 1. 72) This remains true for an arbitrary number of quantum states, hence this result can be expressed for arbitrary number of density matrices.