Qubit state estimation and enhancement by quantum thermal noise

From a qubit in a noisy state affected by an uncontrolled decohering environment represented by a thermal bath at temperature T, estimation of the norm of its Bloch vector is considered, equivalent to estimation of its purity or of its linear entropy. The performance in estimation is assessed by the quantum Fisher information. When the qubit can be prepared with an optimal orientation precisely matched to the thermal noise, the estimation performance always degrades with an increasing temperature of the bath. On the contrary, for a non-optimal orientation of the qubit, the possibility of an enhancement of the estimation performance with an increasing temperature of the bath is demonstrated. Such behaviour shows that increased decoherence is not necessarily associated with poorer informational performance, and can be compared with stochastic resonance or useful noise effects previously reported in classical (non-quantum) estimation.