Abstract
Coherent spaces spanned by a finite number of coherent states are studied. They have properties analogous to coherent states (resolution of the identity, closure under displacement transformations, closure under time evolution transformations, etc.). The set of all coherent spaces is a distributive lattice and also a Boolean ring (Stone’s formalism). The work provides the theoretical foundation, for the description of quantum devices that operate with coherent states and their superpositions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.R. Klauder, B.-S. Skagerstam (eds.), Coherent States (World Scientific, Singapore, 1985)
A. Perelomov, Generalized Coherent States and Their Applications (Springer, Heidelberg, 1986)
S.T. Ali, J.-P. Antoine, J.-P. Gazeau, Coherent States, Wavelets and Their Generalizations, 2nd edn. (Springer, New York, 2014)
A. Vourdas, Coherent spaces, Boolean rings and quantum gates. Ann. Phys. 373, 557 (2016)
G. Birkhoff, J. von Neumann, The logic of quantum mechanics. Ann. Math. 37, 823 (1936)
G. Birkhoff, Lattice Theory (American Mathematical Society, Rhode Island, 1995)
C. Piron, Foundations of Quantum Physics (Benjamin, New York, 1976)
M. Stone, The theory of representations for Boolean algebras. Trans. Am. Math. Soc. 40, 37 (1936)
M. Stone, Applications of the theory of Boolean rings to general topology. Trans. Am. Math. Soc. 41, 375 (1937)
M. Johnstone, Stone Spaces (Cambridge University Press, Cambridge, 1982)
P.R. Halmos, Lectures on Boolean Algebras (Springer, New York, 1963)
R. Sikorski, Boolean Algebras (Springer, New York, 1969)
T.C. Ralph et al., Quantum computation with optical coherent states. Phys. Rev. A68, 042319 (2003)
P. Marek, J. Fiurasek, Elementary gates for quantum information with superposed coherent states. Phys. Rev. A 82, 014304 (2010)
A. Vourdas, The growth of Bargmann functions and the completeness of sequences of coherent states. J. Phys. A 30, 4867 (1997)
A. Vourdas, K.A. Penson, G.H.E. Duchamp, A.I. Solomon, Generalized Bargmann functions, their growth and von Neumann lattices. J. Phys. A 45, 244031 (2012)
A. Vourdas, Mobius operators and non-additive quantum probabilities in the Birkhoff-von Neumann lattice. J. Geom. Phys. 101, 38 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Vourdas, A. (2018). Coherent Spaces. In: Antoine, JP., Bagarello, F., Gazeau, JP. (eds) Coherent States and Their Applications. Springer Proceedings in Physics, vol 205. Springer, Cham. https://doi.org/10.1007/978-3-319-76732-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-76732-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76731-4
Online ISBN: 978-3-319-76732-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)