跨视界关联的存续：非惯性系与黑洞时空中玻色场的反射熵
Surviving correlations across a horizon: reflected entropy for bosonic fields in non-inertial frames and black hole spacetimes
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中文总结 AI 辅助
本文研究非惯性系与黑洞时空中自由玻色场的反射熵与马尔可夫间隙，通过分块对角化得到三种量子态的相关形式，发现其与费米子情形存在显著差异，且黑洞中饱和值与质量无关。
中文摘要 AI 辅助
我们研究自由玻色场模式的反射熵与马尔可夫间隙，该场由惯性观测者（爱丽丝、查理）和匀加速观测者（鲍勃）共享，涉及二分贝尔态及三分沃纳（W）态、格林伯格-霍恩-蔡林格（GHZ）态。与费米子情形不同，玻色子博戈留波夫变换张成具有无限维福克空间，且压缩参数无界。通过识别守恒荷，我们将约化密度矩阵分块对角化为精确二维 sector，得到三种态的闭式或半解析形式。虽已知玻色子纠缠渐近消失，但爱丽丝-鲍勃反射熵却饱和于非零饱和底值，保留存续的经典关联，并收敛至爱丽丝与鲍勃因果不连通伙伴共享的值。关键的是，仅楔间反射熵随压缩参数线性发散，这与费米子情形（其保持有界）形成鲜明对比，而马尔可夫间隙则趋于饱和。该构造可直接推广至史瓦西黑洞，其中饱和值成为与质量无关的常数。
英文摘要
We study the reflected entropy and the Markov gap for modes of a free bosonic field shared by inertial observers (Alice, Charlie) and a uniformly accelerated one (Bob), for a bipartite Bell state and the tripartite Werner (W) and Greenberger--Horne--Zeilinger (GHZ) states. The bosonic Bogoliubov transformation spans an infinite-dimensional Fock space with an unbounded squeezing parameter unlike the fermionic case. By identifying a conserved charge, we block-diagonalize the reduced density matrices into exact two-dimensional sectors, yielding closed or semi-analytic forms for all three states. Although bosonic entanglement is known to vanish asymptotically, the Alice--Bob reflected entropy instead saturates at a nonzero floor, retaining the surviving classical correlation, and converges to the value Alice shares with Bob's causally disconnected partner. Crucially, only the inter-wedge reflected entropy diverges, linearly in the squeezing parameter---the sharp distinction from the fermionic case, where it stays bounded---while the Markov gaps saturate. The construction transfers verbatim to a Schwarzschild black hole, where the saturation values become mass-independent constants.
