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Relativistic quantum speed limit time in dephasing noise

The behavior of quantum speed limit time (QSLT) for a single free spin $-1/2$ particle described by Gaussian wavepackets in the framework of relativity under dephasing noise is investigated. The dephasing noise acts only on the spin degrees of freedom of the spin$-1/2$ particle. In particular, the effects of initial time parameter, rapidity, average momentum and the size of the wavepackets in the presence of the dephasing noise on the dynamics of evolution process are studied. In general, the effects of relativity monotonically decrease the QSLT in time. In the range of large values of average momentum, critical values of both the rapidity and the size of the wavepackets exist at which the QSLT has its minimum value. In the range of small values of the average momentum, the QSLT monotonically decreases with both rapidity and the size of the wavepackets. The decrease of QSLT in a particular range of rapidity and with other relative parameters may be of great interest in employing fast quantum communication and quantum computation.