Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem

Bounds on the distance between a unital quantum channel and the convex hull of unitary channels, with applications to the asymptotic quantum Birkhoff conjecture

Motivated by the recent resolution of Asymptotic Quantum Birkhoff Conjecture (AQBC), we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels. We provide two lower bounds on this distance by employing techniques from quantum information and operator algebras, respectively. We then show how to apply these results to construct some explicit counterexamples to AQBC. We also point out an interesting connection between the Grothendieck's inequality and AQBC.

A category theoretic approach to asymptotic quantum channel approximation and Birkhoff's Theorem

Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace and the identity. We expect these channels to be convex combinations of unitary channels and yet it is known that some channels cannot be written that way. Recent work has suggested that $n$ copies of a single channel might approximate a mixture (convex combination) of unitaries. In this paper we show that $n(n+1)/2$ copies of a symmetric unital quantum chan…

Hierarchy of quantum correlations under non-Markovian dynamics

We investigate the dynamics of quantum correlations (QC) under the effects of reservoir memory, as a resource for quantum information and computation tasks. Quantum correlations of two-qubit systems are used for implementing quantum teleportation successfully, and for investigating how teleportation fidelity, violation of Bell-CHSH inequality, quantum steering and entanglement are connected with each other under the influence of noisy environments. Both Markovian and non-Markovian channels are considered, and it is shown that the decay and revival of correlations follow the hierarchy of quantu…

极端量子态与过程，以及有限维代数中一般谱面体的极值点

Extreme quantum states and processes, and extreme points of general spectrahedra in finite dimensional algebras

本文刻画了一般谱面体的极值点及相应算子秩的界限，应用于量子态、信道和测量等集合，推导出Choi和Parhasarathy等经典结果，并提出了具有一般仿射约束归一化的POVMs概念及其极值刻画。