Transferring elements of a density matrix

We study restrictions imposed by quantum mechanics on the process of matrix-element transfer. This problem is at the core of quantum measurements and state transfer. Given two systems A and B with initial density matrices and r, respectively, we consider interactions that lead to transferring certain matrix elements of unknown into those of the final state of B. We find that this process eliminates the memory on the transferred (or certain other) matrix elements from the final state of A. If one diagonal matrix element is transferred, _aa=_aa, the memory on each nondiagonal element _ab is completely eliminated from the final density operator of A. Consider the following three quantities, Re_ab, Im_ab, and _aa-_bb (the real and imaginary part of a nondiagonal element and the corresponding difference between diagonal elements). Transferring one of them, e.g., Re_ab=Re_ab, erases the memory on two others from the final state of A. Generalization of these setups to a finite-accuracy transfer brings in a trade-off between the accuracy and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations that account for local aspects of the accuracy-disturbance trade-off in quantum measurements. Thus, the general aspect of state disturbance in quantum measurements is elimination of memory on non-diagonal elements, rather than diagonalization. ©2010 The American Physical Society