Dispersive Quantum Systems

Thomas M. Stace, Howard M. Wiseman

Coupling the output of a source quantum system into a target quantum system is easily treated by cascaded systems theory if the intervening quantum channel is dispersionless. However, dispersion may be important in some transfer protocols, especially in solid-state systems. In this paper we show how to generalize cascaded systems theory to treat such dispersion, provided it is not too strong. We show that the technique also works for fermionic systems with a low flux, and can be extended to treat fermionic systems with large flux. To test our theory, we calculate the effect of dispersion on the fidelity of a simple protocol of quantum state transfer. We find good agreement with an approximate analytical theory that had been previously developed for this example.

L. E. Reichl

Robert Fawcett

Lúcio Souza Fassarella

A "dispersive quantum system" is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of dispersive quantum systems within the class of completely positive Markovian quantum systems in finite dimension (through a homogeneous linear equation for the non-Hamiltonian part of the system's Liouvillian). To set the framework, the basic features of quantum mechanics are reviewed focusing on time evolution and also on the theory of completely positive Markovian quantum systems, including Kossakowski-Lindblad's standard form for Liouvillians. After those general considerations, I present a simple example of dispersive two-level quantum system and apply that to describe neutrino oscillation.

Jing-Yuan Liu, Xu Liu, Wei Zhang +1 more

Dispersive optics quantum key distribution (DO-QKD) based on energy-time entangled photon pairs is an important QKD scheme. In DO-QKD, the arrival time of photons is used in key generation and security analysis, which would be greatly affected by fiber dispersion. In this work, we established a theoretical model of the entanglement-based DO-QKD system, considering the protocol, physical processes (such as fiber transmission and single-photon detection), and the analysis of security tests. Based on this theoretical model, we investigate the influence of chromatic dispersion introduced by transmission fibers on the performance of DO-QKD. By analyzing the benefits and costs of dispersion compensation, the system performance under G.652 and G.655 optical fibers are shown, respectively. The results show that dispersion compensation is unnecessary for DO-QKD systems in campus networks and even metro networks. Whereas, it is still required in DO-QKD systems with longer fiber transmission distances.