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 creation to Quantum details concept (pages 11–64):
Chapter three The Classical Capacities of Quantum Channels (pages 65–125):
Chapter four The Quantum potential 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 conversation Networks (pages 362–387):
Chapter 10 contemporary advancements and destiny instructions (pages 388–412):

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Example text

In this space, the state of the quantum system can be described by a unit vector |ψ〉, which is the state vector. Density matrix ρ holds equivalent information to the state vector |ψ〉, hence we can use the density matrix instead of the state vector to describe the quantum system in the Hilbert space. As follows, if a quantum system is in state ρi with probability pi, then the density matrix of the system can be expressed as k ρ= ∑pρ . 57) k i =1 Second Postulate: Evolution The evolution of an isolated system |ψ〉 can be described by a unitary transformation U as ψ → ψ′ =U ψ .

The measurement method that generalizes the entropy of entanglement to mixed states is called the EF entanglement of formation. If we would like to take a look behind the formula, roughly speaking it simply quantifies how many pure EPR states are needed per copy to prepare many copies of the mixed input entangled state. 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.

61) m This postulate can be formalized with density matrices, too. 62) and the ρ′ post-measurement state can be described as ρ′ = M m ρ M m† M m ρ M m† = . , k is unknown) the density matrix of the mixed state after the measurement can be calculated as M (ρ ) = m ∑ M ρM . 64) j =0 Fourth Postulate: Composite Systems If we have several independent subsystems represented by |ψi〉 then the composite system then can be described by means of ⊗ ρi . Similarly, for independent subsystems {ρi} the density matrix of i the composite system is ⊗ ρi .

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