By Prof. Dr. Peter Lambropoulos, Dr. David Petrosyan (auth.)
This ebook is an creation to the 2 heavily similar matters of quantum optics and quantum info. primarily, the actual points of quantum details processing have now develop into an essential component of quantum optics. The booklet offers an easy, self-contained creation to either matters, whereas illustrating the actual rules of quantum details processing utilizing quantum optical platforms. It therefore has an interdisciplinary personality. For the good thing about a much wider viewers and to make the subject material of the e-book available to these with backgrounds except physics, the authors additionally comprise a quick assessment of quantum mechanics. even if a lot of the cloth used the following is usually present in different books, mentioned at quite a few depths, the actual blend of the themes coated during this booklet is exclusive. in addition, a few points of quantum info, for instance these referring to contemporary experiments on hollow space QED and quantum dots, are defined right here for the 1st time in publication form.
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Extra info for Fundamentals of Quantum Optics and Quantum Information
In addition, the result of the measurement can only be one of the eigenvalues of the operator, with a probability determined by the respective coeﬃcient in the expansion of the state vector in terms of eigenvectors of that operator, which is often refereed to as the Born rule. To state this postulate formally, let A be the Hermitian operator, |ai its eigenvectors with eigenvalues ai , and |Ψ the state of the system. 2 Description of Quantum Systems A |Ψ = ai |Ψ ai |ai . 95) where Πi ≡ |ai ai | is the corresponding projection operator.
The evolution operator U(t) acts upon the state vector |Ψ (0) at initial time t = 0 to change it to |Ψ (t) . 126) while the state of the system is that at t = 0. 126), d dU † (t) ∂A dU(t) A(t) = A U(t) + U † (t) U(t) + U † (t) A . dt dt ∂t dt Using the deﬁnition of U and the fact that U and H commute, since U is a function of H, we have d i ∂A A(t) = [HA − AH] + U † U. 128) and is referred to as the Heisenberg equation of motion of operator A. 3 Density Operator So far we have been describing the behavior of quantum systems in terms of state vectors.
In fact, in most cases of physical systems, their state is not pure. A basic reason for this is that the quantum system may have interacted with other systems, which 1 For an illustration of this statement, see Sect. 17). 38 1 Quantum Mechanical Background have resulted in inseparability of the state vectors of individual systems, called entanglement, as discussed below. For the moment, assume that all we know is that the system is in a mixture (not a superposition) of states |Ψ , not necessary orthogonal to each other, each |Ψ having a diﬀerent expansion in the basis of eigenvectors |n .
Fundamentals of Quantum Optics and Quantum Information by Prof. Dr. Peter Lambropoulos, Dr. David Petrosyan (auth.)