Near-Optimal Mixedness Testing with Pauli Measurements

Abstract

We consider a fundamental problem of \emph{mixedness testing}: Given n copies of an N-qubit state ρ, determine whether ρ= 𝕀_d/d or |ρ−𝕀_d/d|₁ ≥ ε with high probability, where d = 2^N. In particular, we focus on performing this task in the practical setting of single-qubit measurements, where measurements are prepared independently on each qubit. We provide a nearly complete picture of single-qubit mixedness tesing by showing n = Θ̃(√(10)^N/ε²). To establish our lower bound, we introduce a measurement-dependent lower bound framework for adaptive single-copy state certification. For the upper bound, we present a randomized Pauli basis measurement protocol, which relies on a new primitive for computationally efficient uniformity testing of correlation-concentrated distributions on the Boolean hypercube. In conjunction, we provide lower and upper bounds for mixedness testing with fixed Pauli measurement protocols.

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BibTeX RIS

BibTeX

@misc{acharya2026nearoptimal,
  title = {{Near-Optimal Mixedness Testing with Pauli Measurements}},
  author = {Jayadev Acharya and Abhilash Dharmavarapu and Yuhan Liu and Nengkun Yu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.18839},
  eprint = {2608.18839},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.18839},
}

RIS

TY  - UNPB
TI  - Near-Optimal Mixedness Testing with Pauli Measurements
AU  - Jayadev Acharya
AU  - Abhilash Dharmavarapu
AU  - Yuhan Liu
AU  - Nengkun Yu
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2608.18839
UR  - https://arxiv.org/abs/2608.18839
AB  - We consider a fundamental problem of \emph{mixedness testing}: Given n copies of an N-qubit state ρ, determine whether ρ= 𝕀_d/d or |ρ−𝕀_d/d|_1 ≥ ε with high probability, where d = 2^N. In particular, we focus on performing this task in the practical setting of single-qubit measurements, where measurements are prepared independently on each qubit. We provide a nearly complete picture of single-qubit mixedness tesing by showing n = Θ̃(√(10)^N/ε^2). To establish our lower bound, we introduce a measurement-dependent lower bound framework for adaptive single-copy state certification. For the upper bound, we present a randomized Pauli basis measurement protocol, which relies on a new primitive for computationally efficient uniformity testing of correlation-concentrated distributions on the Boolean hypercube. In conjunction, we provide lower and upper bounds for mixedness testing with fixed Pauli measurement protocols.
ER  -

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