Classical versus quantum coherence - Discussion

P. Thornton Greenland

Quantum dots are structures engineered to have desirable quantum-mechanical properties. Much of their potential usefulness stems from the ability to design such structures so that their passive properties can be exploited. However, there are many plans to use dots as the basis of a more active quantum engineering, in which the detailed quantum states of the dot's components are manipulated by externally imposed fields. This leads to a new requirement: our ability to model the time development of individual driven quantum systems. I shall discuss some of the problems which arise when single systems, rather than ensembles, are considered and give examples which illustrate the effects of classical and quantum incoherences. I propose a new classification of incoherent processes, based on their effect on individual wave functions.

Peter E. Gordon

Kae Nemoto, Samuel L. Braunstein

Zakaria Bouafia, Hamza Mhamdi, Mostafa Mansour

Lili Wang, Zhengli Chen, Wenhua Wang +1 more

Shuangshuang Fu, Shunlong Luo, Yuan Sun

Coherence and complementarity are two important themes in quantum mechanics, which have been widely and thoroughly investigated. Recently, with the rapid development of quantum information theory, various measures have been introduced for quantitatively studying the coherence and complementarity. However, most of these studies are independent of each other in that they focus on only one theme, for example, the wave-particle duality and Heisenberg uncertainty principle are usually regarded as manifestation of Bohr’s complementary principle, while coherence is a quantum feature closely related to quantum superposition. During the past few years, there has been a flurry of research interest in the study of quantum coherence from the quantum resource-theoretic point of view. In this paper, we establish two information conservation relations and employ them to characterize complementarity and quantum coherence. As an illustration of the main results, we discuss these two themes in the Mach-Zehnder interferometer. Our study reveals that these two quantum themes are closely related to each other. Our main results are listed as follows. Firstly, we establish two information conservation relations, one is based on " Bures distance versus fidelity” and the other based on " symmetry versus asymmetry”. Then we employ these information conservation relations to investigate coherence and complementarity. Specifically, we provide an explanation of the " Bures distance versus fidelity” trade-off relation from the information conservation perspective, establish the link between the information conservation relation and wave-particle duality, and derive the famous Englert inequality concerning " fringe visibility versus path distinguishability” from the information conservation relation. Furthermore, in the general framework of state-channel interaction, we derive " symmetry versus asymmetry” trade-off relation and explain it as an information conservation relation, reveal its intrinsic relations with coherence and complementarity. Lastly, we demonstrate that the two information conservation relations are closely interrelated, and we also discuss the coherence, decoherence and complementarity in the Mach-Zehnder interferometer, explicitly, we reveal that the Bures distance can be regarded as a lower bound of the asymmetry of state-channel interaction while fidelity is an upper bound of the symmetry of state-channel interaction. We expect that our information conservation relation can provide a unified framework for the study of coherence and complementarity.