New uncertainty relations for tomographic entropy: Application to squeezed states and solitons

Abstract

Using the tomographic probability distribution (symplectic tomogram) describing the quantum state (instead of the wave function or density matrix) and properties of recently introduced tomographic entropy associated with the probability distribution, the new uncertainty relation for the tomographic entropy is obtained. Examples of the entropic uncertainty relation for squeezed states and solitons of the Bose--Einstein condensate are considered.

18 pages, 2 figures, to be published in European Physical Journal B

References in corpus (5)

• Symplectic tomography as classical approach to quantum systems
• Alternative commutation relations, star products and tomography
• Reconstructing the density operator by using generalized field quadratures
• Universal Uncertainty Principle in the Measurement Operator Formalism
• Purity-bounded uncertainty relations in multidimensional space -- generalized purity

Cited by in corpus (11)

• An introduction to the tomographic picture of quantum mechanics
• Towards higher precision and operational use of optical homodyne tomograms
• Optical tomography of Fock state superpositions
• Signatures of entanglement in an optical tomogram
• On the quantum information entropies and squeezing associated with the eigenstates of isotonic oscillator
• Estimation of squeezing properties of multiphoton coherent states from optical tomograms
• Quantum Fourier transform and tomographic Renyi entropic inequalities
• Tomographic entropy and cosmology
• Tomography on f-oscillators
• An investigation of nonclassical properties of light using an optical tomogram
• Probability Representation of Quantum Mechanics: Comments and Bibliography