Thermodynamics Of Quantum Information

Maxwell's demon revealed the relationship between entropy and information,demonstrating that by using information one can relax the restrictions imposed by the second law on the energy exchanged between a system and its surroundings.We review the origin,historical evolution as well as the latest developments at the frontiers of scientific research of the ”thermodynamics of information ” regarding Maxwell's demon.The paradox of Maxwell's demon puts forward a challenge to the second law of thermodynamics.After the Landauer's erasure principle,this paradox is solved and information exhibits important influence in physical process.We give examples about the information-acquisition and feedback-control process which involves Maxwell's demon,especially the Szilard engine.We design a heat engine with multi-reservoir,an ancillary system,and quantum memory,from which we derive an inequality related to the second law of thermodynamics and give a limitation on the work gain from the engine by analyzing the entropy change and quantum mutual information change during the process.Then we discuss the case of one-reservoir and two-reservoir respectively.In addition,remarkably,by the combination of two independent engines and with the help of the entropic uncertainty relation with quantum memory,we find that the total maximum work gained from those two heat engines should be larger than a quantity related to the quantum entanglement between the ancillary state and the quantum memory.This result provides a lower bound for the maximum work extracted,in contrast to the upper bound in the conventional second law of thermodynamics.However,the validity of this inequality depends on whether the maximum work can achieve the upper bound.Also we study the second law of thermodynamics from another perspective.First we investigate the fine-grained uncertainty relations for qubit systems by measurements corresponding respectively to two and three spin operators.Then we derive the general bound for a combination of two probabilities of projective measurements in mutually unbiased bases in d-dimensional Hilbert space.All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics.This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.