By Sandor Imre, Laszlo Gyongyosi

Content material:

Chapter 1 advent (pages 1–10):

Chapter 2 creation to Quantum details conception (pages 11–64):

Chapter three The Classical Capacities of Quantum Channels (pages 65–125):

Chapter four The Quantum ability 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 defense and privateness (pages 325–361):

Chapter nine Quantum verbal exchange Networks (pages 362–387):

Chapter 10 contemporary advancements and destiny instructions (pages 388–412):

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**Additional resources for Advanced Quantum Communications: An Engineering Approach**

**Example text**

The entanglement of formation defines the least amount of pure state entanglement needed on average to produce σAB. 129) i where the decomposition of σAB is σ AB = ∑ pi ρi = ∑ pi ψ i ψ i , hence the i i minimization is made overall. 11. To compute entanglement of formation is very complex in practice, and therefore other simpler expressions have been derived, such as the two-qubit formula, the entanglement distillation, or the entanglement cost. A method for the measuring of the arbitrarily unknown two-qubit entanglement of formation formula has been developed, using local operations and classical communication in the measurement process.

In information theory, the relative entropy function is also known as the Kullback-Leibler divergence. 10. The quantum conditional entropies and the quantum mutual information for entangled states. hence it is not a true distance—it measures a pseudodistance. In the classical interpretation, the relative entropy function between probability distributions of random variables A and B gives us the expected number of extra bits required to code A, when using a code based on B—rather than using a code based on A.

As we have seen in this example, the von Neumann entropy that can be extracted from a density matrix containing orthogonal pure states is just the same as the Shannon entropy of a classical bit. 1. 2 Important Properties of the von Neumann Entropy If we apply a unitary transformation U to a density matrix ρ, the transformation does not change the von Neumann entropy of the quantum system S(ρ) = S (UρU † ) . 8. The concavity property of the von Neumann entropy. The von Neumann entropy function has an important property for mixed quantum states associated with the density matrices {ρi} and probability distribution {pi}, then the concavity property of the von Neumann entropy can be expressed in the following way: ∑ p S (ρ ) ≤ S ∑ p ρ .