Control Power Of High-dimensional Controlled Teleportation

Quantum entanglement is an important resource in quantum information processing,and it plays a vital role in many quantum information applications.Among the many important applications of quantum entanglement,controlled quantum teleportation is one of the most important applications.In the controlled quantum teleportation scheme,only with the permission of the controller can the receiver fully receive any quantum state information from the sender with a 100%probability.Since the concept of controlled quantum teleportation was proposed,related theoretical research has been gradually improved.It has interesting applications in various fields of quantum communication,and has made considerable progress in theory and experiments in recent years.This paper focuses on high-dimensional controlled quantum teleportation.By studying arbitrary d-dimensional controlled quantum teleportation scheme via high-dimensional tripartite standard Greenberger-Horne-Zeilinger(GHZ)entangled state channel and GHZ-like entangled channel,the controller's ability to control the effective information transmission process between the sender and receiver is analyzed.The main content of this paper can be summarized as follows:1.For the control power of any d-dimensional controlled quantum teleportation scheme,this paper studies the high-dimensional three-party standard GHZ entangled state channel and GHZ-like entangled state channel.The control power is quantitatively analyzed and the upper limit of the control power in d-dimensional controlled teleportation is determined.Different from the existing research on the range of control power given in the two-dimensional controlled teleportation scheme,this paper focuses on high-dimensional situations,and gives a performance analysis of GHZ-like states from the perspective of control power.In previous work,this type of quantum channel has not been discussed.2.This paper determines the trade-off relationship between the control power and the capacity of the quantum channel.Studies have shown that higher control power can be obtained by reducing the number of dimensions of the information transmitted in the high-dimensional quantum channel or by increasing the number of dimensions of the encoded information of the entangled particles held by the controller.In particular,when transmitting a single qubit in a perfect controlled teleportation scheme,the maximum control power can be achieved in a three-dimensional GHZ-like channel.The value of the maximum control power is larger than the maximum value predicted in the previous work,and is also larger than the upper limit of the control power in the two-dimensional measurement subchannel.This also shows that the original conclusion based on the original two-dimensional metric subchannel will no longer be applicable to the case where the transmission information and channel dimensions are asymmetric in a GHZ-like channel.The standards proposed in this paper are simple,practical,and applicable to all perfectly controlled teleportation schemes using pure state quantum channels.The research in this paper provides a feasible method for obtaining higher control power,and also provides possible new ideas and methods for defining the high-dimensional entanglement of multi-body systems.