QUANTUM PRECISION LIMITS FOR ANY IMPLEMENTATION OF SINGLE QUBIT GATES UNDER CONSERVATION LAWS
Tokishiro Karasawa, Masanao Ozawa, Julio R. Gea-Banacloche, Kae Nemoto · International Journal of Quantum Information · 2008
A quantum gate is implemented by control interactions between qubits and their ancilla system. It has been shown that the control interactions have possibilities to induce the dynamical decoherence on the qubits if an additive conservation law is assumed in the interactions and the ancilla system is finite. This decoherece put the precision limit on the gate, which cannot be removed from the qubit by optimizing the interaction and the initialization of the ancilla system. In this paper, we give the outline of investigating the precision limit which is formulated by the lower bound of the gate infidelity, one minus the squared fidelity, for an arbitrary self-adjoint gate on a single qubit. We show rigorous lower bounds in terms of the variance of the conserved quantity and a simple geometrical relation between the conservation law to be assumed and the gates to be implemented. We also comment on another approach to provide the precision limit for an arbitrary single qubit gate under a conservation law.