A non-Markovian approach for two dissipative quantum walks

Diego de Falco, Dario Tamascelli

Félix Pellerin, Valentin Boettcher, W. A. Coish +1 more

We realize a tunable fiber-loop simulator of the Wigner–Weisskopf model with engineered spectral densities, validate controlled atom–bath dynamics, and implement a dissipative SSH quantum walk, demonstrating topological robustness against non-Markovian coupling to structured, sub-Ohmic photonic environments.

Diego de Falco, Dario Tamascelli, Centro Interdipartimentale +1 more

Tian Chen, Xiong Zhang, Xiangdong Zhang

Quantum walk (QW) provides a versatile platform for the realization of quantum algorithms. Due to the existence of the inevitable noises in the walk, the different quantum algorithms accommodating to different noises are demanded. Thus, the success of the algorithms based on the QW requires us to sense different noises in the walk. Until now, the way to distinguish different noises in the walk has been discussed rarely. Here, we propose an efficient way to sense the noises in the one and two dimensional QWs. The populations of the coin in the walk with or without decoherence are presented. By only detecting the populations of the coin in the QW, we can determine whether there exists the decoherence in the total QW system. Moreover, the non-Markovianity of the coin in the one and two dimensional QWs is revealed, in which the coin is taken as an open quantum system, and the other components of the QW system is taken as the large environment. With the measured value of the non-Markovianity for the coin, we can conjecture which kinds of noise emerges in the one and two dimensional QWs.

Javid Naikoo, Subhashish Banerjee, C. M. Chandrashekar

The quantum channels with memory, known as non-Markovian channels, are of crucial importance for a realistic description of a variety of physical systems, and pave ways for new methods of decoherence control by manipulating the properties of an environment such as its frequency spectrum. In this work, the reduced dynamics of a coin in a discrete-time quantum walk is characterized as a non-Markovian quantum channel. A general formalism is sketched to extract the Kraus operators for a $t$-step quantum walk. Non-Markovianity, in the sense of P indivisibility of the reduced coin dynamics, is inferred from the nonmonotonous behavior of distinguishability of two orthogonal states subjected to it. Furthermore, we study various quantum information-theoretic quantities of a qubit under the action of this channel, putting in perspective the role such channels can play in various quantum information processing tasks.

Dariusz Chruściński, Andrzej Kossakowski