By Dieter Heiss
Quantum details technology is a quickly constructing box that not just delivers a revolution in computing device sciences but in addition touches deeply the very foundations of quantum physics. This e-book involves a suite of lectures via prime specialists within the box that bridges the distance among commonplace textbook fabric and the study literature, hence offering the ne- cessary historical past for postgraduate scholars and non-specialist researchers wishing to familiarize themselves with the topic completely and at a excessive point. This quantity is perfect as a direction booklet for postgraduate scholars, and teachers will locate in it a wide selection of fabric for bringing their classes up-to-date.
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Additional info for Fundamentals of Quantum Information: Quantum Computation, Communication, Decoherence and All That
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J. e. 17) and thus cannot be mimicked by any classical system (see lecture 2). In other words, the effect of interaction with the oscillator has been to lengthen the time scale of the oscillation between the states |↑ and |↓ enormously but to leave its qualitative nature completely unchanged. More generally, the inference from the (near)-vanishing at time t0 of the off-diagonal elements of the single-particle density matrix ρˆ1 to the absence of any effects of interference between the two basis states at a later time is in general invalid.
More generally, the inference from the (near)-vanishing at time t0 of the off-diagonal elements of the single-particle density matrix ρˆ1 to the absence of any effects of interference between the two basis states at a later time is in general invalid. It is justified only in two special cases: (1) there is no term in the Hamiltonian for times later than t0 which couples the two systems (b) there is an interaction term, but the nature of the two states χ which are involved in the entanglement is such that it is ineffective in restoring coherence.
It is also arguably the generic case, since the quantity J(ω) (∼ Im χΩ (ω)) is formally odd in ω, and thus if it is analytic at ω = 0 the leading term in the limit ω → 0 must be linear in ω; in the absence of pathology this term should not vanish. 17) where we note that the quantity α is dimensionless. 17) is often referred to in the literature as “ohmic”: such systems have been intensively studied, in particular in ref. [8]. In that reference it is shown, inter alia, that the value of α = 1 is the discriminant (at zero temperature and in the limit ∆ ωc ) between two qualitatively different types of behavior of σz (t), corresponding respectively to localization (as in the case s < 1) and to Qubits, Cbits, Decoherence, Quantum Measurement and Environment 37 damped (in fact possibly overdamped) oscillation.