从纠缠熵到赝熵
Pseudo entropy from entanglement entropy
- University of Warsaw（华沙大学）
- Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
- Inamori Research Institute for Science（稻盛科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文利用解析延拓和克拉默斯-克勒尼希关系，从普通纠缠熵推导出赝熵的实部和虚部，并应用于共形场论和高斯态，给出超额赝熵及Renyi熵的公式。
AI中文摘要：
赝熵将纠缠熵从单一量子态扩展到一对非正交态，并且通常是复数。利用柯西-黎曼方程、克拉默斯-克勒尼希关系以及态参数中的解析延拓，我们展示了赝熵的实部和虚部如何以及在何种程度上可以从普通纠缠熵推导出来。对于有限维希尔伯特空间中具有全纯系数的族，约化转移矩阵等于在复参数处求值的普通约化密度矩阵公式。然后，一个收敛的泰勒级数从纠缠熵在实中点的偶数和奇数导数给出赝熵的实部和虚部。矩阵恒等式还给出了超额赝熵和Renyi熵的公式，以及具有多项式系数的族的插值公式。我们将这些结果应用于共形场论中的边界态淬火和热态，以及费米子和玻色子高斯态及其淬火。在共形场论中，克拉默斯-克勒尼希关系给出了虚部的一阶矩，用中心荷和边界态的单点函数表示。
英文摘要：
Pseudo entropy extends entanglement entropy from a single quantum state to a pair of nonorthogonal states and is generally complex. Taking advantage of Cauchy-Riemann equations, Kramers-Kronig relations, and analytic continuation in state parameters, we show how and to what extent real and imaginary parts of pseudo entropy can be derived from ordinary entanglement entropy. For families with holomorphic coefficients in finite-dimensional Hilbert spaces, the reduced transition matrix equals the ordinary reduced density matrix formula evaluated at complex parameters. Then a convergent Taylor series gives the real and imaginary parts of pseudo entropy from even and odd derivatives of entanglement entropy at the real midpoint. The matrix identity also gives formulae for excess pseudo entropy and Renyi entropies, and interpolation formulae for families with polynomial coefficients. We apply these results to boundary-state quenches and thermal states in conformal field theory, and to fermionic and bosonic Gaussian states and quenches. In conformal field theory, Kramers-Kronig relations give the first moment of the imaginary part in terms of the central charge and one-point functions for boundary states.
