Abstract
The notions of purity and entropy play a fundamental role in the theory of density operators. These are nonnegative trace class operators with unit trace. We review and complement some results from a rigorous point of view.
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References
G. Adesso, S. Ragy, and A. R. Lee. Continuous variable quantum information: Gaussian states and beyond. Open Systems & Information Dynamics 21, 01n02, 1440001 (2014)
G. S. Agarwal, Entropy, the Wigner distribution function, and the approach to equilibrium of a system of coupled harmonic oscillators. Phys. Rev. A3(2), 828–831 (1971)
M. de Gosson and F. Luef, Symplectic Capacities and the Geometry of Uncertainty: the Irruption of Symplectic Topology in Classical and Quantum Mechanics. Phys. Reps. 484 (2009)
M. de Gosson, Quantum blobs, Found. Phys. 43(4), 440–457 (2013)
M. de Gosson, Symplectic geometry and quantum mechanics. Vol. 166. Springer Science & Business Media (2006)
M. de Gosson, Symplectic methods in harmonic analysis and in mathematical physics. Vol. 7. Springer Science & Business Media (2011)
M. de Gosson, The symplectic camel and phase space quantization. J. Phys. A: Math. Gen. 34(47), 10085 (2001)
M. de Gosson, The symplectic camel and the uncertainty principle: the tip of an iceberg? Found. Phys. 99 (2009)
B. Dutta, N. Mukunda, and R. Simon, The real symplectic groups in quantum mechanics and optics, Pramana 45(6), 471–497 (1995)
G. B. Folland, Harmonic Analysis in Phase space, Annals of Mathematics studies, Princeton University Press, Princeton, N.J. (1989)
Acknowledgements
Maurice de Gosson has been financed by the Grant P27773-N23 of the Austrian Research Foundation FWF.
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de Gosson, M. (2019). On the Purity and Entropy of Mixed Gaussian States. In: Boggiatto, P., et al. Landscapes of Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05210-2_5
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DOI: https://doi.org/10.1007/978-3-030-05210-2_5
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