You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Model Checking Quantum Systems --- A Survey 
Chapter Title:  C. Difficulty in Model Checking Quantum Systems 
1. Abstract of Cited Paper (BIB001):  PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics

Literature Review:
Unfortunately, it seems that the current model-checking techniques cannot be directly applied to quantum systems because of some essential differences between the classical world and the quantum world. To develop model-checking techniques for quantum systems, the following three problems must be systematically addressed: • System modelling and property specification: The classical system modelling method cannot be used to describe the behaviours of quantum systems, and the classical specification language is not suited to formalise the properties of quantum systems to be checked. So, we need to carefully and clearly define a conceptual framework in which we can properly reason about quantum systems, including formal models of quantum systems and formal description of temporal properties of quantum systems. • Quantum measurements: Model-checking is usually applied to check long-term behaviours of the systems. But to check whether a quantum system satisfies a certain property at a time point, one has to perform a quantum measurement on the system, which can change the state of the system. This makes studies of the long-term behaviours of quantum systems much harder than that of classical systems BIB001 , BIB002 ,  . • Algorithms: The state spaces of the classical systems that model-checking algorithms can be applied to are usually finite or countably infinite. However, the state spaces of quantum systems are inherently continuous even when they are finite-dimensional. In order to develop algorithms for model-checking quantum systems, we have to exploit some deep mathematical properties of the systems so that it suffices to examine only a finite number of (or at most countably infinitely many) representative elements, e.g. those in an orthonormal basis, of their state spaces. Also, a linear algebraic structure always resides in the state space of a quantum system. So, an algorithm checking a quantum system should be carefully developed so that the linear algebraic structure will not be broken.