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f-oscillators deformation for Moyal algebras
V. I. Man'ko, G. Marmo, E. C. G. Sudarshan +1
Using general construction of star-product the q-deformed Wigner-Weyl-Moyal quantization procedure is elaborated. The q-deformed Groenewold kernel determining the product of quantu…
The geometry of density states, positive maps and tomograms
V. I. Man'ko, G. Marmo, E. C. G. Sudarshan +1
The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purificatio…
Does The Uncertainty Relation Determine The Quantum State?
Olga V. Man'ko, V. I. Man'ko, G. Marmo +2
The example of nonpositive trace-class Hermitian operator for which Robertson-Schroedinger uncertainty relation is fulfilled is presented. The partial scaling criterion of separabi…
Differential geometry of density states
V. I. Man'ko, G. Marmo, E. C. G. Sudarshan +1
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application…
Partial positive scaling transform: a separability criterion
Olga V. Manko, V. I. Manko, G. Marmo +3
The problem of constructing a necessary and sufficient condition for establishing the separability of continuous variable systems is revisited. Simon [R. Simon, Phys. Rev. Lett. 84…
Entanglement structure of adjoint representation of unitary group and tomography of quantum states
V. I. Man'ko, G. Marmo, E. C. G. Sudarshan +1
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional…