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Sample optimal Quantum identity testing via Pauli Measurements

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arxiv 2009.11518 v1 pith:ODIKIG44 submitted 2020-09-24 quant-ph

Nengkun Yu This is my paper · ORCID
classification quant-ph
keywords epsilonmeasurementspauliquantumsampletestingcdotcomplexity
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abstract

In this paper, we show that $\Theta(\mathrm{poly}(n)\cdot\frac{4^n}{\epsilon^2})$ is the sample complexity of testing whether two $n$-qubit quantum states $\rho$ and $\sigma$ are identical or $\epsilon$-far in trace distance using two-outcome Pauli measurements.

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  1. An Optimal Analysis of the Product Test

    quant-ph 2026-07 accept novelty 7.0 of 10

    For every n >= 2, the product test's worst-case acceptance probability equals (1 + mω^2 + (1−mω)^2)/2 with m = floor(1/ω), where ω is the maximum squared overlap with a product state.

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