Fundamental limits to contrast reversal of self-fidelity correlations

In measurement design, it is common to engineer anti-contrast readouts -- two measurements that respond as differently as possible to the same inputs so that common-mode contributions are suppressed. To assess the fundamental scope of this strategy in unitary dynamics, we ask whether two evolutions can be made uniformly opposite over a broad input ensemble, or whether quantum mechanics imposes a structural limit on such opposition. We address this by treating self-fidelity (survival probability) as a random variable on projective state space and adopting the Pearson correlation coefficient as a device-agnostic measure of global opposition between two evolutions. Within this framework we establish the following theorem: For any nontrivial pair of unitaries, self-fidelity maps cannot be point-wise complementary correlation on the entire state space. Consequently, the mathematical lower edge of the correlation bound is not physically attainable, which we interpret as a unitary-geometric floor on anti-contrast, independent of hardware specifics and noise models. We make this floor explicit in realizable settings. In a single-qubit Bloch-sphere Ramsey model, a closed-form relation shows that a residual common-mode component persists even under nominally optimal tuning. In higher dimensions, Haar/design moment identities reduce ensemble means and covariances of self-fidelity to a small set of unitary invariants, yielding the same conclusion irrespective of implementation details. Taken together, these results provide a model-independent criterion for what anti-contrast can and cannot achieve in unitary sensing protocols.

Publication Details

Journal
ArXiv.org
Published
2025-09-30
Primary Topic
Genomics and Phylogenetic Studies
Type
article
Field-Weighted Citation Impact
0.00

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article

Fundamental limits to contrast reversal of self-fidelity correlations

ArXiv.org
Genomics and Phylogenetic Studies
article

Fundamental limits to contrast reversal of self-fidelity correlations

article en

Abstract

In measurement design, it is common to engineer anti-contrast readouts -- two measurements that respond as differently as possible to the same inputs so that common-mode contributions are suppressed. To assess the fundamental scope of this strategy in unitary dynamics, we ask whether two evolutions can be made uniformly opposite over a broad input ensemble, or whether quantum mechanics imposes a structural limit on such opposition. We address this by treating self-fidelity (survival probability) as a random variable on projective state space and adopting the Pearson correlation coefficient as a device-agnostic measure of global opposition between two evolutions. Within this framework we establish the following theorem: For any nontrivial pair of unitaries, self-fidelity maps cannot be point-wise complementary correlation on the entire state space. Consequently, the mathematical lower edge of the correlation bound is not physically attainable, which we interpret as a unitary-geometric floor on anti-contrast, independent of hardware specifics and noise models. We make this floor explicit in realizable settings. In a single-qubit Bloch-sphere Ramsey model, a closed-form relation shows that a residual common-mode component persists even under nominally optimal tuning. In higher dimensions, Haar/design moment identities reduce ensemble means and covariances of self-fidelity to a small set of unitary invariants, yielding the same conclusion irrespective of implementation details. Taken together, these results provide a model-independent criterion for what anti-contrast can and cannot achieve in unitary sensing protocols.

ArXiv.org
National Research Foundation, Ministry of Science, ICT and Future Planning, Korea Institute of Science and Technology, Korea Institute of Science and Technology Information, National Research Foundation of Korea, Iran Telecommunication Research Center
Openalex Percentile: Top 47%
Genomics and Phylogenetic Studies
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Fundamental limits to contrast reversal of self-fidelity correlations · ArXiv.org (2025) | TGRS Research Map | TGRS