The preservation of quantum coherence is besieged by a fundamental dogma: its revival necessitates non-Markovian memory effects from structured environments. This paradigm has constrained quantum control strategies and obscured simpler paths to coherence protection. Here, we shatter this belief by demonstrating unambiguous coherence revival even in strictly Markovian regimes, achieved solely through basis engineering in the σx/σy bases. We establish a comprehensive analytical framework for predictive coherence control, delivering three universal design principles. First, we derive a minimum critical noise based frequency, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\omega_{0}^{c} \approx {\pi \over {t_{\rm max}}}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msubsup> <mi>ω</mi> <mrow> <mn>0</mn> </mrow> <mrow> <mi>c</mi> </mrow> </msubsup> <mo>≈</mo> <mrow> <mfrac> <mi>π</mi> <mrow> <msub> <mi>t</mi> <mrow> <mi mathvariant="normal">max</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </math></EquationSource> </InlineEquation> serving as a universal criterion for engineering non-Markovian dynamics over any interval [0, tmax]. Crucially, we show that Markovian environments (ω0 < ω<Stack> 0 c </Stack>) can exhibit coherence revival when the Zeeman energy satisfies ωk > π/(2tmax), establishing basis engineering as an independent control dimension that separates revival dynamics from environmental memory. Furthermore, for non-Markovian environments, we provide exact conditions for periodic and complete revival: setting ω0 = n · 6.285/tmax guarantees revival in the σz basis, while combining it with ωk = πω0/6.285 ensures perfect revival in the σx/σy bases. Our results, validated by rigorous quantum simulations, provide a predictive toolkit for coherence control, offering immediate strategies for enhancing quantum memory, sensing, and error mitigation.

Analytical control of quantum coherence: Markovian revival via basis engineering and exact non-Markovian criteria

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发表日期：

2026年1月4日

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Na-Na Zhang,
Chao-Yi Wu,
Ming Li,
Wei-Xuan Cao,
Jun-Hao Zhang,
Ren-Pu Li,
Yong-Rui Guo

摘要

The preservation of quantum coherence is besieged by a fundamental dogma: its revival necessitates non-Markovian memory effects from structured environments. This paradigm has constrained quantum control strategies and obscured simpler paths to coherence protection. Here, we shatter this belief by demonstrating unambiguous coherence revival even in strictly Markovian regimes, achieved solely through basis engineering in the σ_x/σ_y bases. We establish a comprehensive analytical framework for predictive coherence control, delivering three universal design principles. First, we derive a minimum critical noise based frequency, $\omega_{0}^{c} \approx {\pi \over {t_{\rm max}}}$ $ω_{0}^{c} \approx \frac{π}{t_{\max}}$ serving as a universal criterion for engineering non-Markovian dynamics over any interval [0, t_max]. Crucially, we show that Markovian environments (ω₀ < ω ₀ ^c ) can exhibit coherence revival when the Zeeman energy satisfies ω_k > π/(2t_max), establishing basis engineering as an independent control dimension that separates revival dynamics from environmental memory. Furthermore, for non-Markovian environments, we provide exact conditions for periodic and complete revival: setting ω₀ = n · 6.285/t_max guarantees revival in the σ_z basis, while combining it with ω_k = πω₀/6.285 ensures perfect revival in the σ_x/σ_y bases. Our results, validated by rigorous quantum simulations, provide a predictive toolkit for coherence control, offering immediate strategies for enhancing quantum memory, sensing, and error mitigation.