Quantum Memory Assisted Entropic Uncertainty Relations And Their Applications

The uncertainty relation is a core concepts in quantum theory. Uncertainty relations capture the essence of the inevitable randomness associated with the out-comes of two incompatible quantum measurements. Using entrophy to measure the quantum fluctuation of observables leads to the entropic form of uncertainty relations, as known as the entropic uncertainty relations (EURs). In recent years, EURs have gained importance because of their operational applications for pri-vacy issues in cryptographic tasks, in the detection of entangled states, and in constructing error-correcting codes for communicating quantum or private classi-cal information. It may be noted that the possibility of violating the uncertainty relation using an entangled pair was conceived as early as1934by Karl Popper who had proposed an experiment to do so. The quantum memory assisted EURs identified recently by Berta et al has proved the Karl’s propose.If the system is maximally entangled with its memory, the outcomes of two incompatible mea-surements made on distinct and identical copies of such a state can be predicted precisely by an observer with access to the quantum memory. This paper will use the theory of quantum memory assisted EURs to optimize the lower bound of EURs and it’s application.The main works and innovation points are as follows:In chapter One, I briefly described the basic theories related to this thesis research, which include the basic theories of the Heisenberg Uncertainty Relation, Quantum Information Entropy and Entropy Uncertainty Relation.In chapter Two, What I showed is about the studies on the quantum entropy uncertainty relation supported by quantum memory. By introducing quantum memory into the entropy uncertainty relation and using the entanglement between the system under test and quantum memory, the lower limit of entropy uncertainty relation is optimized. In theory, when the system and quantum memory are in the maximum entanglement, the lower limit of the uncertainty relation can be reduced to zero.In chapter three, I focus on the applications of optimized quantum memory assisted EURs,such as their operational applications for privacy issues in crypto-graphic tasks, in the detection of entangled states, in constructing error-correcting codes for communicating quantum or private classical information, etc.In chapter four, I studied the optimization of the quantum memory assisted EURs. Add the difference between the state’s quantum Discord and it’s classical correlation into the lower bound of the quantum memory assisted EURs. we can see that by measuring the difference one can optimize the EURs:s lower bound freely. We call the situation that the quantum Discord is larger than the classical correlation the "tightening", otherwise we call it reduce.In chapter five, it’s the summary of the thesis and the outlook of this topic are given.