By Sandor Imre, Laszlo Gyongyosi
Chapter 1 creation (pages 1–10):
Chapter 2 advent to Quantum details 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 safety and privateness (pages 325–361):
Chapter nine Quantum communique Networks (pages 362–387):
Chapter 10 fresh advancements and destiny instructions (pages 388–412):
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Additional info for Advanced Quantum Communications: An Engineering Approach
Before we start to discuss the density operator, we introduce some terms. An n × n square matrix A is called positive-semidefinite if 〈ψ |A|ψ〉 is a non-negative real number for every vector |ψ 〉. λn} eigenvalues of A are all non-negative real numbers then it is positivesemidefinite. This definition has an important role in quantum information theory, since every density matrix is positive-semidefinite. It means, for any vector |ψ〉 the positive-semidefinite property says that n ϕ ρϕ = ∑p i n ϕ ψi ψi ϕ = i =1 ∑p i ϕ ψi 2 ≥ 0.
This measures the entanglement of the mixed state from another approach. 11. Entanglement of formation measures the entanglement as the number of pure EPR states that are needed to prepare many copies of the mixed input entangled state. quantity gives us the minimum of the number of pure entangled pairs that are required to generate copies from the original mixed state. The entanglement cost EC is the asymptotic formula of the entanglement of formation. 130) i where EF is the entanglement of formation function, ε(ρAB) is the von Neumann entropy of entanglement, and n is the number of output EPR states.
An interesting historical fact is that the HSW theorem from 1997 used the concept of Holevo information, which was discovered about twenty-five years before, in 1973. Holevo in 1998 used the same definition of subspaces as Bennett in 1999; however, he applied it to a completely different problem. 2 BASIC DEFINITIONS AND FORMULAS In this section, we summarize the basic definitions and formulas of quantum information theory. Those readers who are familiar with density matrices, entropies, and the like may run through this chapter and focus only on notations (the collection of the notations used in this book can be found in Notations and Abbreviations) and can return later if it is required when processing another chapter.