arXiv subjects

Kamil Yu. Magadov

Publications and source records attributed to Kamil Yu. Magadov.

4 recordsLinked to original sources

arXiv2019

Spin polarization-scaling quantum maps and channels

We introduce a spin polarization-scaling map for spin-$j$ particles, whose physical meaning is the decrease of spin polarization along three mutually orthogonal axes. We find conditions on three scaling parameters under which the map is positive, completely positive, entanglement breaking, 2-tensor-stable positive, and 2-locally entanglement annihilating. The results are specified for maps on spin-$1$ particles. The difference from the case of spin-$\frac{1}{2}$ particles is emphasized.

quant-ph↗

arXiv2019

Matrix Bailey Lemma and the Star-Triangle Relation

We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help of residue calculus we explicitly show how the integral Bailey lemma can be reduced to its matrix version. As a consequence, we demonstrate that the matrix Bailey lemma can be interpreted as a star-triangle relation, or as a Coxeter relation for a permutation group.

math.CA↗

arXiv2017

Absolutely separating quantum maps and channels

Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U \varrho U^†$. By example of a three qubit system we show that in multipartite scenario neither full separability implies bipartite absolute separability nor the reverse statement holds. The main goal of the paper is to analyze quantum maps resulting in absolutely separable output states. Such absolutely separating maps affect the states in a way, when no Hamiltonian dynamics can make them entangled afterwards. We study general properties of absolutely separating maps and channels with respect to bipartitions and multipartitions and show that absolutely separating maps are not necessarily entanglement breaking. We examine stability of absolutely separating maps under tensor product and show that $Φ^{\otimes N}$ is absolutely separating for any $N$ if and only if $Φ$ is the tracing map. Particular results are obtained for families of local unital multiqubit channels, global generalized Pauli channels, and combination of identity, transposition, and tracing maps acting on states of arbitrary dimension. We also study the interplay between local and global noise components in absolutely separating bipartite depolarizing maps and discuss the input states with high resistance to absolute separability.

quant-ph↗

arXiv2017

Positive tensor products of qubit maps and n-tensor-stable positive qubit maps

We analyze positivity of a tensor product of two linear qubit maps, $Φ_1 \otimes Φ_2$. Positivity of maps $Φ_1$ and $Φ_2$ is a necessary but not a sufficient condition for positivity of $Φ_1 \otimes Φ_2$. We find a non-trivial sufficient condition for positivity of the tensor product map beyond the cases when both $Φ_1$ and $Φ_2$ are completely positive or completely co-positive. We find necessary and (separately) sufficient conditions for $n$-tensor-stable positive qubit maps, i.e. such qubit maps $Φ$ that $Φ^{\otimes n}$ is positive. Particular cases of 2- and 3-tensor-stable positive qubit maps are fully characterized, and the decomposability of 2-tensor-stable positive qubit maps is discussed. The case of non-unital maps is reduced to the case of appropriate unital maps. Finally, $n$-tensor-stable positive maps are used in characterization of multipartite entanglement, namely, in the entanglement depth detection.

quant-ph↗