It is shown that dynamical equations for quantum tomograms retain the normalization conditions of their solutions during evolution only if the solutions satisfy a set of special conditions. These conditions are found explicitly. On the contrary, it is also shown that the classical Liouville equation, Moyal equation for Wigner function, and evolution equation for Husimi function retain normalization of any initially normalized and quickly decaying at infinity functions on the phase space. Other necessary and sufficient conditions for optical and symplectic tomogram-like functions to be tomograms of physical states are discussed.It is shown that dynamical equations for quantum tomograms retain the normalization conditions of their solutions during evolution only if the solutions satisfy a set of special conditions. These conditions are found explicitly. On the contrary, it is also shown that the classical Liouville equation, Moyal equation for Wigner function, and evolution equation for Husimi function retain normalization of any initially normalized and quickly decaying at infinity functions on the phase space. Other necessary and sufficient conditions for optical and symplectic tomogram-like functions to be tomograms of physical states are discussed.

arXiv:1606.07132Jun 22, 20160 citations

Some necessary conditions for quantum-state tomograms

E. Nahvifard, M. R. Bazrafkan

Journal of Russian Laser ResearchMay 1, 20121 citation

Unnormalized Tomograms and Quasidistributions of Quantum States

Vladimir I. Man’ko, Liubov A. Markovich

We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan P-functions, and the Husimi Q-functions, that violate the standard normalization condition for probability distribution functions. We introduce special conditions for theWigner function to determine the tomogram with the Radon transform and study three different examples of states like the de Broglie plane wave, the Moshinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta function, the Airy function, and Fresnel integrals violate the standard normalization condition and the density matrix of the state therefore cannot always be reconstructed. We propose a method that allows circumventing this problem using a special tomogram in the limit form.We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan P-functions, and the Husimi Q-functions, that violate the standard normalization condition for probability distribution functions. We introduce special conditions for theWigner function to determine the tomogram with the Radon transform and study three different examples of states like the de Broglie plane wave, the Moshinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta function, the Airy function, and Fresnel integrals violate the standard normalization condition and the density matrix of the state therefore cannot always be reconstructed. We propose a method that allows circumventing this problem using a special tomogram in the limit form.

Theoretical and Mathematical PhysicsNov 1, 20181 citation

Tomograms in the quantum–classical transition

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +2 more

arXiv:quant-ph/0505220Physics Letters AJun 15, 200523 citations

Quantum-Like Behavior of Classical Systems

Thomas Filk A

Lecture notes in computer scienceJan 1, 20129 citations

Unnormalized quasi-distributions and tomograms of quantum states

V. I. Man'ko, Liubov A. Markovich

Tomograms and quasi-distribution functions like Wigner, Glauber - Sudarshan $P$ - and Husimi $Q$ - functions that violate the standard normalization condition are considered. Conditions under which a reconstruction of the density matrix using these tomograms and quasi-distribution functions is possible are obtained. Three different examples of states like the de Broglie plane wave, the Moschinsky shutter problem and the stationary state of the charged particle in the uniform and constant electric field are studied. Their tomograms and quasi-distribution functions expressed in terms of the Dirac delta function, the Airy function and the Fresnel integrals are shown to violate the standard normalization condition and thus the density matrix of the state can not always be reconstructed.Tomograms and quasi-distribution functions like Wigner, Glauber - Sudarshan $P$- and Husimi $Q$- functions that violate the standard normalization condition are considered. Conditions under which a reconstruction of the density matrix using these tomograms and quasi-distribution functions is possible are obtained. Three different examples of states like the de Broglie plane wave, the Moschinsky shutter problem and the stationary state of the charged particle in the uniform and constant electric field are studied. Their tomograms and quasi-distribution functions expressed in terms of the Dirac delta function, the Airy function and the Fresnel integrals are shown to violate the standard normalization condition and thus the density matrix of the state can not always be reconstructed.

arXiv:1708.04847Aug 16, 20170 citations

Tomograms and quasi-distribution functions like Wigner, Glauber - Sudarshan

P

- and Husimi

Q

- functions that violate the standard normalization condition are considered. Conditions under which a reconstruction of the density matrix using these tomograms and quasi-distribution functions is possible are obtained. Three different examples of states like the de Broglie plane wave, the Moschinsky shutter problem and the stationary state of the charged particle in the uniform and constant electric field are studied. Their tomograms and quasi-distribution functions expressed in terms of the Dirac delta function, the Airy function and the Fresnel integrals are shown to violate the standard normalization condition and thus the density matrix of the state can not always be reconstructed.