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Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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TL;DR: In this paper, the state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states, which are generated by the various Veronese embeddings of the underlying state space into higher-dimensional state spaces.
Abstract: The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of the underlying state space into higher-dimensional state spaces. This construction is applied to the parameterisation of generalised coherent states, which is useful for practical calculations and provides an elementary combinatorial approach to the geometry of the coherent state space. The results are extended to Hilbert spaces with indefinite inner products, leading to the introduction of a new kind of generalised coherent states.
16 citations
TL;DR: In this paper, the authors present the full characterization of phase-randomized or phase-averaged coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols.
Abstract: We present the full characterization of phase-randomized or phase-averaged coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols. We report on the suitable formalism to analytically describe the main features of these states and on their experimental investigation, that results in agreement with theory. In particular, we consider a recently proposed non-Gaussianity measure based on the quantum fidelity, that we compare with previous ones, and we use the mutual information to investigate the amount of correlations one can produce by manipulating this class of states.
16 citations
TL;DR: In this paper, the master field becomes the Boltzmann field in the free Fock space and the quantum semigroup SUq(2) becomes a central element of the quantum group bialgebra.
Abstract: In recent works by Singer, Douglas, Gopakumar and Gross an application of results of Voiculescu from noncommutative probability theory to constructions of the master field for large-N matrix field theories have been suggested. It turns out that this master field becomes the Boltzmann field in the free Fock space. In this note we consider interrelations between the master field and quantum semigroups. We define the master field algebra and observe that it is isomorphic to the algebra of functions on the quantum semigroup SUq(2) for q=0. The master field becomes a central element of the quantum group bialgebra. The quantum Haar measure on the SUq(2) for any q gives the Wigner semicircle distribution for the master field. Coherent states on SUq(2) become coherent states in the master field theory.
16 citations
TL;DR: In this article, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of the oscillation depends on the energy.
Abstract: The notion of f-oscillators generalizing q-oscillators is discussed. For the classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of the oscillation depends on the energy. The f-coherent states generalizing the q-coherent states are constructed. Applied to quantum optics, the photon distribution function and photon number means and dispersions are calculated for the f-coherent states as well as the Wigner-Moyal function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck's distribution formula.
16 citations
TL;DR: In this article, the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state is investigated and an upper bound for the von Neumann entropy for a bipartition (A,B) of a quantum system and conditions to saturate it are given.
Abstract: Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state We find an upper bound for the von Neumann entropy for a bipartition (A,B) of a quantum system and conditions to saturate it We show that these states can be interpreted as ground states of generic Hamiltonians or as the physical states in a quantum gauge theory and that under specific conditions their geometric entropy satisfies the entropic area law If G is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (ie, bipartite) graph states and they include Greenberger-Horne-Zeilinger, cluster states, etc Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states
16 citations