Quantum decoherence and entanglement in Markov and non-Markov systems

Robert Joynt, Bich Ha Nguyen, Văn Hiếu Nguyễn

Robert Joynt, NguyenVan Hieu, Nguyen Bich Ha +3 more

Zhang, Tian Li

The main purpose of this thesis is to discuss quantum decoherence in the frame- work of operator algebras. We will define several types of decoherence of quantum Markov systems based on the original notion introduced by Ph. Blanchard and R. Olkiewicz; then we will give a number of suffiecient conditions for a quantum Markov system to display decoherence, and explain the relation between them.

Ivan Bardet, Marius Junge, Nicholas D. LaRacuente +2 more

Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable in general. Much recent work has focused on upper bounding certain capacities in terms of more tractable quantities such as specific norms from operator theory. In the meantime, there has also been substantial recent progress on estimating decoherence times with techniques from analysis and geometry, even though many hard questions remain open. In this article, we introduce a class of continuous-time quantum channels that we called transferred channels, which are built through representation theory from a classical Markov kernel defined on a compact group. In particular, we study two subclasses of such kernels: Hörmander systems on compact Lie-groups and Markov chains on finite groups. Examples of transferred channels include the depolarizing channel, the dephasing channel, and collective decoherence channels acting on d qubits. Some of the estimates presented are new, such as those for channels that randomly swap subsystems. We then extend tools developed in earlier work by Gao, Junge and LaRacuente to transfer estimates of the classical Markov kernel to the transferred channels and study in this way different non-commutative functional inequalities. The main contribution of this article is the application of this transference principle to the estimation of decoherence time, of private and quantum capacities, of entanglement-assisted classical capacities as well as estimation of entanglement breaking times, defined as the first time for which the channel becomes entanglement breaking. Moreover, our estimates hold for non-ergodic channels such as the collective decoherence channels, an important scenario that has been overlooked so far because of a lack of techniques.

A.‐S. F. Obada, Abdel‐Baset A. Mohamed, Hosney A. Hessein