Abstract:

To construct a tight frame for a given vector, quantum joint measurement of teleportation was investigated, and a construction method of tight frame was proposed, which was promoted and applied in classical and quantum field. The generalized construction method of tight frame based on quantum joint measurement: Firstly, arrange the given vector into a coefficient matrix,then get its left unitary, right unitary and singular value matrix by singular value decomposition. Secondly, find a base including a column whose coefficient matrix is just the non-zero part of the singular value matrix. At the end, arrage the rest colomns of the base into non-zero part of the singular value matrix, then get the rest tight frame columns by singular value reconstruction.

Key words: quantum information, tight frame, joint measurement, teleportation