Abstract:

The construction methods of tight frame in quantum field is researched according to the finite-dimensional tight frame in classic field.As one-to-one correspondence between tight frames and rank-one generalized quantum measurement is proved，two construction methods of tight frame in quantum field based on generalized quantum measurement are designed.Studies show that two optimal quantum tight frame can separately solve two basic strategies of state discrimination which are minimum error discrimination and optimal unambiguous discrimination. The minimum error discrimination of a given set of vectors using generalized quantum measurement method with the least–squares criteria is precisely quantum tight frame based on least squares measurement，which can be divided into two situations:constrained least-squares frame (CLSF) that has specified scale and unconstrained least-squares frame (ULSF) whose scale is chosen to minimize the least-squares error.Quantum tight frame based on optimal unambiguous discrimination is also given using quantum generalized measurement method.Finally, an example is given to compare these optimal construction methods of tight frame and illustrate that ULSF is best.

Key words: optical communication, tight frame, least-squares, quantum measurement