arXiv subjects

Michal Banacki

Publications and source records attributed to Michal Banacki.

4 recordsLinked to original sources

arXiv2023

On steering in the C*-algebraic framework

We discuss a scenario of bipartite steering with local subsystems of the parties modeled by certain operator algebras. In particular, we formalize the notion of quantum assemblages in a commuting observables paradigm and focus on equivalent descriptions of such objects providing a systematic analysis of previously scattered approaches. We provide necessary and sufficient conditions for the equivalence of quantum commuting and tensor models that is stable under extensions of the trusted subsystem by arbitrary finite-dimensional ancillae. As a result, we show that the gap between two models of bipartite steering can be observed in an arbitrary scenario with two measurement settings ($m = 2$) and more than two outcomes ($k > 2$). We also demonstrate that the identified gap is independent of nonlocality arising from the refutation of Tsirelson's conjecture. Finally, we provide no-go results concerning the possibility of post-quantum steering in this most general bipartite paradigm and discuss related corollaries regarding free probability and operator system approach as well as a link to Tsirelson's problem.

quant-ph↗

arXiv2020

Information backflow may not indicate quantum memory

We analyze recent approaches to quantum Markovianity and how they relate to the proper definition of quantum memory. We point out that the well-known criterion of information backflow may not correctly report character of the memory falsely signaling its quantumness. Therefore, as a complement to the well-known criteria, we propose several concepts of elementary dynamical maps. Maps of this type do not increase distinguishability of states which are indistinguishable by von Neumann measurements in a given basis. Those notions and convexity allows us to define general classes of processes without quantum memory in a weak and strong sense. Finally, we provide a practical characterization of the most intuitive class in terms of the new concept of witness of quantum information backflow.

quant-ph↗

arXiv2018

Necessary and sufficient condition of separability for D-symmetric diagonal states

For multipartite states we consider a notion of D-symmetry. For a system of $N$ qubits it concides with usual permutational symmetry. In case of $N$ qudits ($d\geq 3$) the D-symmetry is stronger than the permutational one. For the space of all D-symmetric vectors in $(\mathbb{C}^d)^{\otimes N}$ we define a basis composed of vectors $\{|R_{N,d;k}\rangle: \,0\leq k\leq N(d-1)\}$ which are analog for Dicke states. The aim of this paper is to discuss the problem of separability of D-symmetric states which are diagonal in the basis $\{|R_{N,d;k}\rangle\}$. We show that if $N$ is even and $d\geq 2$ is arbitrary then a PPT property is necessary and sufficient condition of separability for D-invariant diagonal states. In this way we generalize results obtained by Yu for qubits. Our strategy is to use some classical mathematical results on a moment problem.

quant-ph↗

arXiv2017

Quantum symmetry groups of noncommutative tori

We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative $n$-torus $\mathbb{T}_θ^n$ in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of compact quantum groups $\mathbb{G}_θ=(A_θ^n,Δ)$ such that for each $θ$, $\mathbb{G}_θ$ is the final object in the category of all compact quantum groups acting on $\mathbb{T}_θ^n$ in a filtration preserving way. We describe in details the structure of the C*-algebra $A_θ^n$ and provide a concrete example of its representation in bounded operators. Moreover, we compute the Haar measure of $\mathbb{G}_θ$. For $θ=0$, the quantum group $\mathbb{G}_0$ is nothing but the classical group $\mathbb{T}^n\rtimes S_n$, where $S_n$ is the symmetric group. For general $θ$, $\mathbb{G}_θ$ is still an extension of the classical group $\mathbb{T}^n$ by the classical group $S_n$. It turns out that for $n=2$, the algebra $A_θ^2$ coincides with the algebra of the quantum double-torus described by Hajac and Masuda. Using a variation of the little subgroup method we show that irreducible representations of $\mathbb{G}_θ$ are in one-to-one correspondence with irreducible representations of $\mathbb{T}^n\rtimes S_n$.

math.OA↗