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In this paper, we present a polynomial-complexity algorithm to construct aspecial orthogonal matrix for the deterministic remote state preparation (DRSP)of an arbitrary n-qubit state, and prove that if n>3, such matrices do notexist. Firstly, the construction problem is split into two sub-problems, i.e.,finding a solution of a semi-orthogonal matrix and generating allsemi-orthogonal matrices. Through giving the definitions and properties of thematching operators, it is proved that the orthogonality of a special matrix isequivalent to the cooperation of multiple matching operators, and then theconstruction problem is reduced to the problem of solving an XOR linearequation system, which reduces the construction complexity from exponential topolynomial level. Having proved that each semi-orthogonal matrix can besimplified into a unique form, we use the proposed algorithm to confirm thatthe unique form does not have any solution when n>3, which means it isinfeasible to construct such a special orthogonal matrix for the DRSP of anarbitrary n-qubit state.

Infeasibility of constructing a special orthogonal matrix for the deterministic remote preparation of arbitrary n-qubit state