Compression for Qubit Clocks

Abstract

Two-Ievel (qubit) clock systems are often used to perform precise measurement of time. In this work, we propose a compression protocol for n identically prepared states of qubit clocks. The protocol faithfully encodes the states into (1/2) log n qubits and (1/2) log n classical bits and works even in the presence of noise. If the purity of the clock states is fixed, (1/2) log n qubits are sufficient. We also prove that this protocol requires the minimum amount of total memory among all protocols with vanishing error in the large n limit.