Streaming quantum state purification

TL;DR

This paper introduces an efficient, recursive quantum state purification protocol for qudits of any dimension, suitable for streaming data, with asymptotically optimal sample complexity in reducing errors.

Contribution

It develops a novel purification method based on the swap test that works for qudits of any dimension and is optimal in sample complexity.

Findings

Protocol is asymptotically optimal in final error parameter

Applicable in streaming scenarios with minimal quantum memory

Works for qudits of any dimension

Abstract

Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.