  In this contribution, we introduce a technique to freeze the parameters which
describe the accelerated states between two users to be used in the context of
quantum cryptography and quantum teleportation. It is assumed that, the two
users share different dimension sizes of particles, where we consider a
qubit-qutrit system. This technique depends on local operations, where it is
allowed that each particle interacts locally with a noisy phase channel. We
show that, the possibility of freezing the information of quantum channel
between the users depends on the initial state setting parameters, the initial
acceleration parameter strength of the phase channel. It is shown that, one may
increase the possibility of freezing the estimation degree of the parameters if
only the larger dimension system or both particles pass through the noisy phase
channel. Moreover, at small values of initial acceleration and large values of
the channel strength, the size of freezing estimation areas increases. The
results may be helpful in the context of quantum teleportation and quantum
coding.
