For composite quantum systems, we consider quantum channels that uniquely determine the channels of subsystems. Such channels of composite systems are called generating quantum channels.
The talk is devoted to properties of those quantum channels. We give a criterion for a quantum channel to be generating. Algebraic and topological properties of sets of generating quantum channels are...
This talk is devoted to homogeneous random walks on a line. In the classical case, the generating function for the positive half-line first passage time is discussed. It often turns out to admit an algebraic equation and is useful in statistical computations. Besides, the corresponding algebraic curve sometimes is rational and has a positive genus which can be accounted via analyzing...
The talk is devoted to one method to derive the equation of stochastic dynamics of a quantum system for a wave function and its applications in quantum information theory. The main example of stochastic dynamics is the process of continuous-time weak measurements of an observable $L=L^*$ described
by the stochastic differential Belavkin equation
$ d|\psi_t\rangle =-iH|\psi_t\rangle...
We build POVM, which is absolutely continuous relative to the scalar measure with a projector-valued density, and study the quantum channel generated by it. Also, we consider the possibility of restoring states when measured by the Davis--Lewis instrument. An experiment with two outcomes is considered, and we compare two cases: with post-selection and without post-selection. We study how...
There are many faces of $C^*$-algebras whose symmetries encode important aspects of their structures. We show that in surprisingly different situations these symmetries are implemented by Jordan $*$-isomorphisms and lead to full Jordan invariants. In this respect we study the following structures: one dimensional projections in a Hilbert space with transition probability and orthogonality...
We propose a framework in which quantum measurement is applied to a subsystem of an entangled state, thus producing a quantum ensemble in the other part. This approach generalizes the seminal multibeam Young's interference experiment
which established the wave-particle duality principle, connecting quantum properties (interference) and path information. Our framework provides a connection...
Recently, classical capacity of quantum channels generated by projective unitary irreducible representations of finite group was calculated for some strong limitations of the group structure, on the representation $U_g$, on the probability distribution $\pi_g$, on the finite group $G$ and finally that the obtained channel $\Phi_G$ has to be covariant with respect
to representation $U_g$.
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We show that multiqubit quantum channels which may be realised via stabilizer circuits without classical control (Clifford channels) have a particularly simple structure. They can be equivalently defined as channels that preserve mixed stabilizer states, or the channels with stabilizer Choi state. Up to unitary encoding and decoding maps any Clifford channel is a product of stabilizer state...
