Entropy decrease in Quantum Zeno Effect

If a measurement process is regarded as an irreversible process, then by Second law of thermodynamics the entropy should increase after any measurement process. By the same spirit a quantum system undergoing repeated measurement should show strong irreversibility leading to entropy production. On the contrary we show that in quantum Zeno effect setting the entropy of a quantum system decreases and goes to zero after a large number of measurements. We discuss the entropy change under continuous measurement model and show that entropy can decrease if we use a more accurate measuring apparatus. email:[email protected] Since its inception the concept of the entropy of a state has played an important role in understanding enigmas of physics in diverse areas such as thermodynamics, quantum mechanics, information theory and recently in the area of quantum information processing. Traditionally one associates some sort of “disorder” with entropy of a physical system. The hallmark of second law of thermodynamics is that the entropy of an isolated system increases with time or remains constant. However, it increases only when a system undergoes an irreversible process (which in turn attributes an arrow of time). In terms of negentropy this should decrease for an irreversible dynamical changes in the system. Given a quantum system, if it is left undisturbed and allowed to evolve unitarily then the entropy remains constant with respect to a given preparation. This is rigidly connected with the principle of linearity of time evolution of quantum system, because one [1] could show that if the time evolution equation is non-linear then entropy of a mixture of quantum system could spontaneously decrease in a closed system. But what about the entropy of a quantum system under observation? Since observation(measurement) on a quantum system is an irreversible process one would say that the entropy should increase as was first discussed by von Neumann [2] in formulating his measurement theory. The entropy change occuring in an isolated quantum system without measurement and entropy increase due to measurement are quite different as expounded in a lucid book by Brillouin [3]. In the later case some amount of information can be obtained as measurement involves an experiment with system and apparatus. Thus, the information