Compression for Qubit Clocks

TL;DR

This paper introduces a compression protocol for qubit clock states that efficiently encodes multiple copies into fewer qubits and classical bits, maintaining accuracy even with noise, and proves its optimality in memory usage.

Contribution

The work presents a novel compression protocol for qubit clocks that is both efficient and proven to be optimal in memory requirements for large systems.

Findings

Protocol encodes $n$ states into $(1/2) \, \log n$ qubits and classical bits.

Works reliably even with noisy states.

Achieves minimal total memory among all vanishing-error protocols.

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.