By Mark Fannes (auth.), Erwin Brüning, Francesco Petruccione (eds.)
ISBN-10: 3642028705
ISBN-13: 9783642028700
ISBN-10: 3642028713
ISBN-13: 9783642028717
Based on 8 broad lectures chosen from these given on the well known Chris Engelbrecht summer time institution in Theoretical Physics in South Africa, this article at the theoretical foundations of quantum info processing and conversation covers an array of themes, together with quantum chances, open structures, and non-Markovian dynamics and decoherence. It additionally addresses quantum details and relativity in addition to checking out quantum mechanics in excessive strength physics.
Because those self-contained lectures speak about issues no longer often coated in complicated undergraduate classes, they're excellent for post-graduate scholars coming into this box of analysis. many of the lectures are written at a extra introductory point whereas others are offered as tutorials that survey contemporary advancements and leads to a number of subfields.
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Additional resources for Theoretical Foundations of Quantum Information Processing and Communication: Selected Topics
Example text
We can now wonder when such a Markovian behaviour can be expected. Under which assumptions can one prove that a reduced dynamics is Markovian? This question is answered by the theories of weak coupling and singular coupling limits. Further questions concern the classification of Markovian semi-groups and their generators. Fortunately, quantum operations which arise as above have an additional property which is deeply connected with quantum mechanics, namely complete positivity. This makes the analysis of semi-groups and their generators feasible, at least under some technical conditions.
From Lidskii’s theorem, that the eigenvalues of ρ + σ are within distance from the eigenvalues of ρ and hence still positive for sufficiently small. Therefore ρ belongs to the interior of the density matrices. Suppose conversely that Det(ρ) = 0; then at least one eigenvalue of ρ is equal to 0. This implies that however small > 0, there always exists a σ with σ = σ † , tr σ = 0 and σ ≤ such that ρ + σ has at least one strictly negative eigenvalue. We have therefore shown that ρ lies on the boundary of the state space.
Position observable As an example of an observable in the sense outlined above we now want to introduce the position observable. Rather than relying on the usual correspondence principle with respect to classical mechanics, we want to give an operational definition of the position observable, fixing its behavior with respect to the action of the relevant symmetry group, which in this case is the isochronous Galilei group, containing translations, rotations and boosts, that is to say velocity transformations.
Theoretical Foundations of Quantum Information Processing and Communication: Selected Topics by Mark Fannes (auth.), Erwin Brüning, Francesco Petruccione (eds.)
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