Purest Quantum State Identification

TL;DR

This paper introduces a new framework for identifying the least noisy quantum states among multiple unknown states, using adaptive and coherent measurement strategies to improve accuracy and quantify quantum memory advantages.

Contribution

It formulates a rigorous paradigm for purest quantum state identification, deriving optimal algorithms and bounds that demonstrate the power of coherent measurements over incoherent strategies.

Findings

Adaptive algorithm achieves exponentially decreasing error with N

Coherent measurement protocol outperforms incoherent strategies

Lower bounds show limitations of fixed two-outcome incoherent POVMs

Abstract

Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification, which can be used to improve the accuracy of quantum computation and communication. We formulate a rigorous paradigm for identifying the purest quantum state among $K$ unknown $n$-qubit quantum states using total $N$ quantum state copies. For incoherent strategies, we derive the first adaptive algorithm achieving error probability $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$, fundamentally improving quantum property learning through measurement optimization. By developing a coherent measurement protocol with error bound $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, we demonstrate a significant separation from incoherent strategies, formally quantifying the power of quantum memory and coherent measurement. Furthermore, we establish a lower bound by demonstrating that all strategies with fixed two-outcome incoherent POVM must suffer error probability exceeding $ \exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This research advances the characterization of quantum noise through efficient learning frameworks. Our results establish theoretical foundations for noise-adaptive quantum property learning while delivering practical protocols for enhancing the reliability of quantum hardware.