![]() ![]() For instance, when considering the channel 41, the l 1 norm of coherence for with n 2 = 0 is frozen during the entire evolution when q 1 = 1 (i.e., the bit flip channel). ![]() In fact, for with certain n 2 r−1 = 0 (or n 2 r = 0), simplifies to (or ). Moreover, for certain special initial states, the freezing condition presented in Corollary 4 may be further relaxed. These results are hoped to add another facet to the already rich theory of decoherence and shed light on revealing the interplay between structures of quantum channel and geometry of the state space, as well as how they determine quantum correlation behaviors of an open system.īy establishing rigorously the sets of incoherent states which are diagonal in the reference basis and q( t) contains the information on ’s structure and its coupling with the system. We also showed that this FR applies to many other coherence and correlation measures. By employing this FR, we further identified condition on the quantum channel for freezing coherence. We first classify the general d-dimensional states into different families and then prove a FR which holds for them. In this work, we aimed at solving this problem. Then, it is natural to ask whether there exists similar FR for various coherence monotones. Remarkably, the evolution equations for certain entanglement monotones (or their bounds) 32, 33, 34, 35, 36, 37, 38, 39, 40 and geometric discords 41 were found to obey the factorization relation (FR) for specific initial states. Looking for general law determining the evolution equation of coherence can facilitate the design of effective coherence preservation schemes. Second, coherence itself is a precious resource for many new quantum technologies, but the unavoidable interaction of quantum devices with the environment often decoheres the input states and induces coherence loss, hence damage the superiority of these quantum technologies 31. First, coherence represents a basic feature of quantum states and underpins all forms of quantum correlations 1. One major goal of quantum theory is to find effective ways of maintaining the amount of coherence within a system. Some other progresses about coherence quantifiers include their connections with quantum correlations 18, 19, 20, their behaviors in noisy environments 21, 22, their local and nonlocal creativity 23, 24, their distillation 25, 26 and the role they played in the fundamental issue of quantum mechanics 27, 28, 29, 30. This sets the stage for quantitative analysis of coherence, which were carried out mainly around the identification of various coherence monotones 11, 12, 13, 14, 15, 16 and their calculation 17. ![]() Very recently, the characterization and quantification of quantum coherence from a mathematically rigorous and physically meaningful perspective has been achieved 10. However, coherence and quantum correlations are in fact different. Sometimes, coherence behaviors were also analyzed indirectly via various quantum correlation measures 3. ![]() But due to the lack of rigorous coherence measures, studies in this subject were usually limited to the qualitative analysis. It also finds support in the promising subject of thermodynamics 4, 5, 6, 7, 8 and quantum biology 9.Ĭlarifying the decoherence mechanism of an noisy system is an important research direction of quantum mechanics. Physically, coherence constitutes the essence of quantum correlations (e.g., entanglement 2 and quantum discord 3) in bipartite and multipartite systems which are indispensable resources for quantum communication and computation tasks. Quantum coherence, an embodiment of the superposition principle of states, lies at the heart of quantum mechanics and is also a major concern of quantum optics 1. ![]()
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