Complex numbers are widely used in classical and quantum physics.Further,they play an important role in describing quantum systems and their dynamical behaviors.Herein,we propose several measures of the imaginarity of...Complex numbers are widely used in classical and quantum physics.Further,they play an important role in describing quantum systems and their dynamical behaviors.Herein,we propose several measures of the imaginarity of quantum states based on l1 norm and convex functions in the framework of resource theory.Further,we investigate the quantum state order after a quantum system passes through a real channel.Rigorous proof shows that these proposed measures possess all the desirable properties for a measure of imaginarity.The connection between the measure of imaginarity based on the l1 norm and the measure of imaginarity based on relative entropy is derived.Moreover,we demonstrate that the l1 norm-based and the relative entropy-based measures of imaginarity are of the same order for qubit quantum states.Further we discuss the influences of the bit flip channel,phase damping channel,and amplitude flip channel on single qubit state order.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62271189,and 12071110)the Science and Technology Project of Hebei Education Department(Grant No.ZD2021066)the Hebei Central Guidance on Local Science and Technology Development Foundation of China(Grant No.226Z0901G)。
文摘Complex numbers are widely used in classical and quantum physics.Further,they play an important role in describing quantum systems and their dynamical behaviors.Herein,we propose several measures of the imaginarity of quantum states based on l1 norm and convex functions in the framework of resource theory.Further,we investigate the quantum state order after a quantum system passes through a real channel.Rigorous proof shows that these proposed measures possess all the desirable properties for a measure of imaginarity.The connection between the measure of imaginarity based on the l1 norm and the measure of imaginarity based on relative entropy is derived.Moreover,we demonstrate that the l1 norm-based and the relative entropy-based measures of imaginarity are of the same order for qubit quantum states.Further we discuss the influences of the bit flip channel,phase damping channel,and amplitude flip channel on single qubit state order.
