# Purest Quantum State Identification

arXiv: https://arxiv.org/abs/2502.14334 · HTML: https://mlsanity.com/paper/2502.14334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Simple Bayesian Algorithms for Best Arm Identification](https://mlsanity.com/paper/1602.08448/) (2016)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Online Learning of Quantum States](https://mlsanity.com/paper/1802.09025/) (2018)
- [Entanglement is Necessary for Optimal Quantum Property Testing](https://mlsanity.com/paper/2004.07869/) (2020)
- [Toward Instance-Optimal State Certification With Incoherent Measurements](https://mlsanity.com/paper/2102.13098/) (2021)
- [Tight Bounds for Quantum State Certification with Incoherent Measurements](https://mlsanity.com/paper/2204.07155/) (2022)
- [On the sample complexity of purity and inner product estimation](https://mlsanity.com/paper/2410.12712/) (2024)
- [How to Construct Random Unitaries](https://mlsanity.com/paper/2410.10116/) (2024)
- [Quantum Channel Certification with Incoherent Strategies](https://mlsanity.com/paper/2303.01188/) (2023)

## Abstract (arXiv)

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 expleft(- Omegaleft(fracN H1log(K) 2n right) right), fundamentally improving quantum property learning through measurement optimization. By developing a coherent measurement protocol with error bound expleft(- Omegaleft(fracN H2log(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  expleft( - Oleft(fracNH12nright)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.