  In this work we give a $(n,n)$-threshold protocol for sequential secret
sharing of quantum information for the first time.
  By sequential secret sharing we refer to a situation where the dealer is not
having all the secrets at the same time, at the beginning of the protocol;
however if the dealer wishes to share secrets at subsequent phases she/he can
realize it with the help of our protocol. First of all we present our protocol
for three parties and later we generalize it for the situation where we have
$(n>3)$ parties.
  Further in a much more realistic situation, we consider the sharing of qubits
through two kinds of noisy channels, namely the phase damping channel (PDC) and
the amplitude damping channel (ADC). When we carry out the sequential secret
sharing in the presence of noise we observe that the fidelity of secret sharing
at the $k^{th}$ iteration is independent of the effect of noise at the
$(k-1)^{th}$ iteration. In case of ADC we have seen that the average fidelity
of secret sharing drops down to $\frac{1}{2}$ which is equivalent to a random
guess of the quantum secret. Interestingly, we find that by applying weak
measurements one can enhance the average fidelity. This increase of the average
fidelity can be achieved with certain trade off with the success probability of
the weak measurements.

Quantum Physics