量子Rényi-Jarzynski等式
Quantum Rényi-Jarzynski Equality
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中文总结 AI 辅助
本文推导了非破坏性量子Jarzynski等式即Rényi-Jarzynski等式，将其用作量子最优控制的可调代价函数，最小化有限量子系统的浴偏离与串扰，揭示了Rényi阶数对浴分布区域的敏感性及相关纠缠要求。
中文摘要 AI 辅助
Jarzynski等式建立了非平衡功与平衡自由能变化之间的严格联系，然而其典型的量子表述依赖于会破坏相干性的测量协议。在本文中，我们运用资源理论方法推导了一种基于任意浴可观测量结果的非破坏性量子Jarzynski等式，由此得到Rényi-Jarzynski等式，该等式通过Rényi k-散度量化有限浴在非绝热驱动下偏离平衡的程度。我们进一步证明，Rényi-Jarzynski等式可作为量子最优控制问题的可调代价函数，适用于需要最小化浴偏离的场景，如态制备和门设计，能最小化有限量子系统中的串扰。我们的玩具模型显示，对于k的某个临界值，竞争极小值之间存在转变，这表明Rényi阶数可调节对浴分布不同区域的敏感性。值得注意的是，当驱动参数在浴能级间变化时，最小化浴偏离需要产生系统-浴纠缠。
英文摘要
The Jarzynski equality provides a strict link between nonequilibrium work and equilibrium free energy changes. Its typical quantum formulations, however, rely on measurement protocols that destroy coherence. In this Letter, we use the resource-theoretic approach to derive a non-destructive quantum Jarzynski equality conditioned on the outcomes of an arbitrary bath observable. This yields the Rényi-Jarzynski equality, which quantifies a finite bath's drift from equilibrium under a non-adiabatic drive via the Rényi $k$-divergence. We further demonstrate that the Rényi-Jarzynski equality provides a tunable cost function for quantum optimal control problems where minimizing bath drift is desired, such as state preparation and gate design, enabling the minimization of cross-talk in finite quantum systems. Our toy model exhibits a transition between competing minima for some critical value of $k$, illustrating how the Rényi order tunes sensitivity to different regions of a bath distribution. Strikingly, when drive parameters vary across bath energy levels, minimizing bath drift requires generating system-bath entanglement.
