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Grigori Amosov

Publications and source records attributed to Grigori Amosov.

11 recordsLinked to original sources
arXiv2024

On characteristics of mixed unitary channels being additive or multiplicative with respect to taking tensor products

We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output states of channels. A class of channels has been allocated for which the use of entangled states doesn't give any advantage under taking supremum and infimum for output characteristics of channels. In particular, $l_p$-norms are multiplicative and the minimal entropy is additive with respect to taking tensor products of channels. As an important application of the obtained results the classical capacity of channel is calculated in the evident form. We compare our techniques with the informational characteristics of Boson quantum channels.

quant-ph↗
arXiv2023

On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures

In this work, we show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers. For this, the concept of perturbation by covariant operator-valued measure in a Banach space is introduced and integral representation of the perturbed semigroup is explicitly constructed. Various physically meaningful examples are provided. In particular, a model of the perturbed dynamics in the symmetric (boson) Fock space is developed as covariant measure for a semiflow of shifts and its perturbation in the symmetric Fock space, and its properties are investigated. Another example may correspond to the Koopman-von Neumann description of a classical oscillator with bounded phase space.

quant-ph↗
arXiv2023

On constructing informationally complete covariant positive operator-valued measures

We study positive operator-valued measures generated by orbits of projective unitary representations of locally compact Abelian groups. It is shown that integration over such a measure defines a family of contractions being multiples of unitary operators from the representation. Using this fact it is proved that the measures are informationally complete. The obtained results are illustrated for the measure with density taking values in the set of coherent states.

quant-ph↗
arXiv2022

On quantum channels generated by covariant positive operator-valued measures on a locally compact group

We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $\hat G$. The method is based upon the Pontryagin duality allowing to establish an isometrical isomorphism between the space of Hilbert-Schmidt operators in $L^2(G)$ and the Hilbert space $L^2(\hat G\times G)$. Any such a measure determines a pair of hybrid (containing classical and quantum parts) quantum channels consisting of the measurement channel and the channel transmitting an initial quantum state to the ensemble of quantum states on the group. It is shown that the second channel can be called a complementary channel to the measurement channel.

quant-ph↗
arXiv2022

On quantum tomography on locally compact groups

We introduce quantum tomography on locally compact Abelian groups $G$. A linear map from the set of quantum states on the $C^*$-algebra $A(G)$ generated by the projective unitary representation of $G$ to the space of characteristic functions is constructed. The dual map determining symbols of quantum observables from $A(G)$ is derived. Given a characteristic function of a state the quantum tomogram consisting a set of probability distributions is introduced. We provide three examples in which $G={\mathbb R}$ (the optical tomography), $G={\mathbb Z}_n$ (corresponding to measurements in mutually unbiased bases) and $G={\mathbb T}$ (the tomography of the phase). As an application we have calculated the quantum tomogram for the output states of quantum Weyl channels.

quant-ph↗
arXiv2020

On classical capacity of Weyl channels

The additivity of minimal output entropy is proved for the Weyl channel obtained by the deformation of a q-c Weyl channel. The classical capacity of channel is calculated.

quant-ph↗
arXiv2006

On strong superadditivity for a class of quantum channels

Given a quantum channel $Φ$ in a Hilbert space $H$ put $\hat H_Φ(ρ)=\min \limits_{ρ_{av}=ρ}Σ_{j=1}^{k}π_{j}S(Φ(ρ_{j}))$, where $ρ_{av}=Σ_{j=1}^{k}π_{j}ρ_{j}$, the minimum is taken over all probability distributions $π=\{π_{j}\}$ and states $ρ_{j}$ in $H$, $S(ρ)=-Trρ\logρ$ is the von Neumann entropy of a state $ρ$. The strong superadditivity conjecture states that $\hat H_{Φ\otimes Ψ}(ρ)\ge \hat H_Φ(Tr_{K}(ρ))+\hat H_Ψ(Tr_{H}(ρ))$ for two channels $Φ$ and $Ψ$ in Hilbert spaces $H$ and $K$, respectively. We have proved the strong superadditivity conjecture for the quantum depolarizing channel in prime dimensions. The estimation of the quantity $\hat H_{Φ\otimes Ψ}(ρ)$ for the special class of Weyl channels $Φ$ of the form $Φ=Ξ\circ Φ_{dep}$, where $Φ_{dep}$ is the quantum depolarizing channel and $Ξ$ is the phase damping is given.

quant-ph↗
arXiv2004

Non-Markov Excursion Set Model of Dark Matter Halo Abundances

The excursion set model provides a convenient theoretical framework to derive dark matter halo abundances. This paper generalizes the model by introducing a more realistic merging and collapse process. A new parameter regulates the influence of the environment and thus the coherence (non-Markovianity) of the merging and the collapse of individual mass shells. The model mass function also includes the effects of an ellipsoidal collapse. Analytic approximations of the halo mass function are derived for scale-invariant power spectra with the slopes $n=0,-1,-2$. The $n=-2$ mass function can be compared with the results obtained from the `Hubble volume' simulations. A significant detection of non-Markovian effects is found for an assumed accuracy of the simulated mass function of 10%.

astro-ph↗