Advanced Quantum Communications: An Engineering Approach by Sandor Imre, Laszlo Gyongyosi

By Sandor Imre, Laszlo Gyongyosi

Content material:
Chapter 1 creation (pages 1–10):
Chapter 2 advent to Quantum info concept (pages 11–64):
Chapter three The Classical Capacities of Quantum Channels (pages 65–125):
Chapter four The Quantum means 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 protection and privateness (pages 325–361):
Chapter nine Quantum verbal exchange Networks (pages 362–387):
Chapter 10 fresh advancements and destiny instructions (pages 388–412):

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8 Quantum Rényi-Entropy As we have seen, the quantum informational entropy can be defined by the S(ρ) von Neumann entropy function. On the other hand, another entropy function can also be defined in the quantum domain; it is called Rényi-entropy and is denoted by R(ρ). This function has relevance mainly in the description of quantum entanglement. 124) where r ≥ 0. R(ρ) is equal to the von Neumann entropy function S(ρ) if lim R ( ρ ) = S ( ρ ) . 125) If parameter r converges to infinity, then we have lim R ( ρ ) = − log ( ρ ) .

One can use a pure state ρ to recover mixed state σ from it, after the effects of environment are traced out. With the help of the partial trace operator, Bob, the receiver, can decouple the environment from his mixed state, and the original state can be recovered by discarding the effects of the environment. If Bob’s state is a probabilistic mixture σ = ∑ pi ϕ i ϕ i , then a global pure purification state |Ψ〉 exists, i which from Bob’s state can be expressed as σ = Trenvironment Ψ Ψ . 5, state σ can be recovered from |Ψ〉 after discarding the environment.

As has been stated by von Neumann and presented in the figure, the decomposition of a mixed state is not unique, since it can be expressed as a mixture of {ρ1, ρ2} or equivalently of {ρ3, ρ4}. One can use a pure state ρ to recover mixed state σ from it, after the effects of environment are traced out. With the help of the partial trace operator, Bob, the receiver, can decouple the environment from his mixed state, and the original state can be recovered by discarding the effects of the environment.

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