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In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the infinite-dimensional case. The properties of the conditional entropy such as monotonicity, concavity and subadditivity are also generalized to the infinite-dimensional case.
The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and the $chi$
The thermal equilibrium distribution over quantum-mechanical wave functions is a so-called Gaussian adjusted projected (GAP) measure, $GAP(rho_beta)$, for a thermal density operator $rho_beta$ at inverse temperature $beta$. More generally, $GAP(rho)$
We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator $-d^2/dx^2$ on $L^2[-a,a]$, $a>0$, that is, the one dimensional infinite square well. First of all, we classify these
The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $mathcal{N}$ with finite spectrum is analysed in detail. The Hamiltonian genera
An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden associated with on