Theory Of Indefinite Causal Order And Its Application In Parameter Estimation Of Quantum Channel

Traditionally,quantum theory assumes that causal structures are deterministic,that is,there is a definite causal order between events.However,if the laws of quantum mechanics are applied to causal relations,the causal order between events is not always fixed,but is subjected to quantum uncertainty.This indefinite causal structure makes new quantum information processing tasks possible and provides methodological tools in quantum of gravity theory.Based on such background,Oreshkov and his coauthors proposed a new quantum theoretical framework that assumes that the quantum theory is locally valid,and is without considering the global space-time causal structure.In this framework,relevant studies have demonstrated that there are quantum correlations which are incompatible with any definite causal order.At the same time,the quantum correlations can violate the so called casual inequality and have been validated experimentally.However,so far,there are few studies on the correlation of causal correlation.Analogous to the study of Bell's nonlocality,this thesis investigates the dependence of causal correlation with the parameters by studying the violation of causal inequality in multiple input and output cases.On the other hand,the quantum switch is used as a tool to study the effect of indefinite causal order on parameter estimation of some quantum channels.Firstly,the communication task is interpreted as a causal game,by introducing a causal game with two players and multi-settings(multi-inputs and multi-outputs,the input number has been extended to 2~nin this thesis),calculate the upper bound of the success probability of the game under the condition that all events are subject to the definite causal order,and establish the corresponding causal inequality;then,under the framework of the process matrix(that is,assuming the local validity of quantum mechanics without considering the global causal order between the experimenters),it is proved that the causal inequality can be violated within the scope of quantum mechanics,that is,the obtained bipartite quantum correlation is compatible with the indefinite casual order.Secondly,the causal game with three players was introduced,the upper bound of the success probability of the causal game is calculated under the causal strategy,and the corresponding tripartite causal inequality with multi-settings is established;it is proved that there are appropriate process matrix and quantum instruments which can violate these causal inequalities in the framework of process matrix.In particular,by applying these strategies,the success probability of the casual game is 1,which means that the players can always win perfectly without considering the global causal order,and the obtained violation is the maximum.Finally,corresponding research work is carried out aiming at the application of indef-inite causal order in parameter estimation of quantum channel.Based on quantum Fisher information,the condition about indefinite causal order has no effect on channel estima-tion is obtained on the basis of the Kraus representation of quantum channel and quantum switch.The influences of indefinite casual order on parameter estimation of two types of noise channels are investigated and discussed.Our results indicate that indefinite causal order has an advantage in improving the parameters estimation precision of the first type of noise channel;for the second type of noise channel,the estimation accuracy depends on the control bit.In addition,the estimation of two non-commutative unitary channels with common unknown parameters is studied,the results indicate that the simultaneous estimation(sequential protocols)is superior to the estimation which is performed sepa-rately,and indefinite causal order is more beneficial to improve the estimation accuracy than the definite casual order for simultaneous estimation.