Tech Notes
Are Mixed States and Random Sampling of States Equivalent?
A tech note comparing a mixed-state ensemble with trajectory sampling, where each run picks one ensemble member at random, as in Pauli twirling. A single-qubit RX noise example shows how variances differ between twirled-effective and trajectory pictures; the general derivation then shows that mean outcomes and the shot-noise variance of estimated probabilities, p(1-p)/N, are the same in both constructions.
- Worked example: RX noise twirled over {I, Y}, with variances for raw, noisy, twirled and trajectory cases
- Mixed-state ensemble vs. random-trajectory state, using Iverson brackets and expectations over the choice
- Sample statistics: empirical probability, sample mean and variance, entropy estimators
- The shot-noise result and the bias in summed squared probabilities
Summary and key points drafted by a language model from the slides, not yet reviewed by me. The slides are the source.
Cite
@techreport{minevndt25,
author = {Zlatko K. Minev},
title = {{Are Mixed States and Random Sampling of States Equivalent?}},
type = {Technical Note},
number = {T25},
institution = {Zlatko's Quantum Notebook},
url = {https://zlatko-minev.github.io/zlatko-minev-quantum-repository/items/t25-are-mixed-states-and-random-sampling-of-states/}
}Reuse
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