Q2. What future works have the authors mentioned in the paper "Measurements in quantum mechanics" ?
Thirdly, the model predicts previously unsuspected coherent magnetic complement of a newly coherent QSC formulation of the weak dispersion interaction between e-pairs, despite their spin-singlet coupling which should ( conventionally ) close out the possibility of any residual magnetic interaction. It remains to the future therefore to consider appropriate formulation of the ‘ equations of matter-wave motion ’ in which the QSC model provides its insights without requiring the assumption of the empirical phenomenon of particle mass. Thirdly, the model predicts previously unsuspected coherent magnetic complement of a newly coherent QSC formulation of the weak dispersion interaction between e-pairs, despite their spin-singlet coupling which should ( conventionally ) close out the possibility of any residual magnetic interaction. It remains to the future therefore to consider appropriate formulation of the ‘ equations of matter-wave motion ’ in which the QSC model provides its insights without requiring the assumption of the empirical phenomenon of particle mass.
Q3. What is the preferred basis in a quantum system?
Using the Markovian Master equation for a harmonic oscillator coupled to a heat bath and the criterion of the predictability sieve Zurek argues that coherent states emerge as the preferred basis.
Q4. What is the definition of entanglement in quantum mechanics?
In quantum information and quantum computation, entanglement is viewed as a resource for computing tasks that can be performed faster or in a more secure way than is classically possible and there are intensive experimental efforts to create entangled states in the labarotory.
Q5. What is the effect of coupling with the environmental degrees of freedom?
the coupling with the environmental degrees of freedom causes decoherence of the pure density matrix of the entangled state into a statistical mixture.
Q6. What is the preferred basis in a quantum-measurement-like scenario?
In the literature, the preferred basis has been variously described as the one in which the final state density matrix becomes diagonal or that set of basis states which are characterized by maximum stability or a minimum increase in linear or statistical entropy, decided by a predictability sieve(Zurek et al. , 1993).
Q7. What is the definition of a pure entangled state of the system and the apparatus?
This pure entangled state of the system and the apparatus is akin to a ’Schroödinger cat state’ which contains one-to-one correlations between the system and ’macroscopic’ apparatus states with all quantum coherences intact.
Q8. What is the role of the environmental influence in destroying the quantum coherences?
The authors have seen that the environmental influence is crucial in not only destroying the quantum coherences, but also is selecting a special state or a preferred basis.
Q9. What is the effect of the inclusion of environmental interaction on the density matrix?
the inclusion of environmental interaction has destroyed the quantum corelations (signified by the off-diagonal elements of the density matrix) and rendered the reduced system-apparatus combine into a statistical mixture.
Q10. What is the Hamiltonian describing this model?
The Hamiltonian describing this model is:H = λσz + p22m + �zσz. (11)While the first two terms represent the self Hamiltonians of the system and apparatus, respectively, the last term is the interaction Hamiltonian.
Q11. How can the authors explain the random motion of a suspended particle?
The random motion of the suspended particle can be statistically explained by taking into account its interaction with a large number of particles which constitute the reservoir of liquid molecules or the ’environment’.
Q12. What is the density matrix for an initial system-apparatus state?
The density matrix for an initial system-apparatus state described by (14), evolving via the master equation (18) has the formρS+A = |a|2| ↑��↑ |ρ↑↑(z, z�, t) + |b|2| ↓��↓ |ρ↓↓(z, z�, t) + [ ab∗| ↑��↓ |ρ↑↓(z, z�, t) + a∗b| ↓��↑ |ρ↓↑(z, z�, t). ] e−αt3 . (19)Here the off-diagonal elements of the density matrix (last two terms) contain a multiplicative factor of the form e−αt3 which causes the decay of these terms to zero over a characteristic time making the density matrix diagonal in spin space.
Q13. What is the importance of the harmonic oscillator apparatus model?
In particular, it is important to look at systems like the harmonic oscillator apparatus model which is fairly generic and exact solutions make it an interesting candidate to explore experimentally in the context of decoherence and quantum measurements.