Quantum Coherence And Quantum State Discriminations

Wave-particle duality is the cornerstone of quantum mechanics.The fact that a physical system is both a wave and a particle has been widely accepted,while coherence characterizes the former.Coherence can also be regards as a resource that plays an important role in quantum information and quantum computation.Coherence theory has been studied for many years in the field of optics,but the quantitative theory has only emerged in recent years.In 2014,Baumgratz et al.proposed a resources theory framework to study coherence in Ref.[1].In addition,quantum state discrimination(QSD)is always a fundamental problem in quantum mechanics.In this paper,we focus on a family of coherence measures and its relations to quantum state discrimination.A question that is commonly asked in all areas of physics is how a certain prop-erty of a physical system can be used to achieve useful tasks and how to quantify the amount of such a property in a meaningful way.In coherence theory,we answer this question by introducing a family of coherence measures and establishing the correspondence between coherence theory and QSD,which also offers nice physical meaning for two coherence measures.Based on these two measures,besides,we es-tablish the complementary relations between coherence and path distinguishability,which gives a quantitative expression for wave-particle duality.The main content is as follows:In chapter 2,we prove that the geometric coherence of a quantum state is equal to the minimum error probability to distinguish a set of pure states with von Neumann measurement.On the contrary,discriminating a set of pure states can also be transformed into the problem of calculating the geometric coherence of a quantum state.This correspondence gives a nice operational meaning to geometric coherence.In the n-slit Young's interference experiment,by choosing the coherence of the system and the path of the particle through the slit to describe the wave and particle property respectively,we establish a new complementary relation between geometric coherence and path distinguishability.This complementarity relation gives a quantitative characterization of wave-particle duality.In chapter 3,we introduce a new family of coherence measures:?-affinity of coherence(0<?<1).When ?= 1/2,we prove that the coherence is equal to the minimum error probability to discriminate a set of pure states with least square measurement.This conclusion gives the operating interpretation of 1/2-affinity of coherence.In addition,we prove that least square measurement is optimal in the sense of asymptotic.Finally,we establish a complementary relationship between 1/2-affinity of coherence and path distinguishability in some special cases.In chapter 4,We first,prove that,the fidelity distance and affinity distance satisfy strong monotonicity.Resource quantification based on these distances can be used to quantify the general quantum resource.While we need to make two as-sumptions,the framework is still sufficiently general,and its special case include the resource theory of entanglement,coherence,partial coherence,and superposition.At last,more importantly,we establish the correspondence between partial coher-ence and mixed state discrimination,and give a physical interpretation for both fidelity partial coherence and affinity partial coherence.This conclusion extends the corresponding result in chapter 2 to the general mixed state case.