Overview And Application Of Quantum Bayesianism

Quantum mechanics is the basic theory that describes the structure,motion and evolution law of the microcosmic world.It is thought to be the two pillar of modern physics with theory of relativity,and its birth has brought a series of important scientific discoveries and technological inventions,such as the emergence of quantum cryptography,the invention of lasers and transistors,etc.However,physicists have never reached agreement on the interpretation of quantum mechanics,the main interpretations are Copenhagen interpretation,many-worlds interpretation and hidden variable interpretation.In 2001,Caves,Fuchs and Schack used Bayes' theorem to interpret quantum mechanics.On this basis,they established quantum Bayesianism(QBism).This theory not only brings a new perspective to the interpretation of quantum mechanics,but also gives a reasonable explanation for the phenomenon of "collapse of wave function" in quantum mechanics.After that,Benavoli,Facchini and Zaffalon verify that quantum mechanics is the extension of Bayes' theorem in the complex Hilbert space under the framework of gambling,which promotes the development of quantum Bayesianism.This paper reviews the research methods and achievements of quantum Bayesianism by analyzing the relevant literature of Caves,Fuchs,Benavoli and Facchini,and focuses on the establishment of quantum Bayesianism and the Bayesian interpretation of quantum state and quantum measurement under the framework of gambling.Caves,Fuchs and Schack have established the quantum Bayesianism under the inspiration of Bayesian probability.The core of this theory is to consider the quantum probability as the subjective probability.By the Gleason's theorem,there is a quantum state corresponding to the above quantum probability,thus indirectly explaining that the quantum state can be regarded as the subjective belief of the rational individual.This paper reviews the theory of subjective probability before introducing quantum Bayesianism,and explains the rationality of subjective probability by introducing Dutch book argument,thus providing theoretical support for quantum Bayesianism.The research methods of Benavoli,Facchini and Zaffalon are different from those of Caves,Fuchs and others.They generalize the imprecise probability model in the classical probability statistics to the quantum,and construct the quantum credal set by the dual relation,thus the subjective form of the quantum state is directly obtained.This paper introduces how Benavoli,Facchini and Zaffalon get the subjective form ofquantum state and quantum measurement under the framework of gambling,and clarifies that quantum states can be interpreted as subjective beliefs of rational agent and quantum measurement can be interpreted as rational agent updating their subjective beliefs.In order to explore how Benavoli,Facchini and Zaffalon use dual relations to construct a quantum credal set,this paper also reviews the imprecise probability model of Williams and Walley,and shows that the duality relationship between quantum credal set and coherent set of desirable gambles is similar to that in the classical case.At the end of this paper,we introduce the application of quantum Bayesianism in quantum inference,and compare Bayesian inference with quantum inference.