A quantum system subject to continuous measurement and postselection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the strength of postselection, this non-Hermitian Hamiltonian can undergo a spectral phase transition. On one side of this phase transition (for weak postselection), an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which $PT$ symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.

中文翻译：

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非厄尔米特量子力学中的纠缠和净化跃迁

受连续测量和后选择影响的量子系统根据非厄米哈密顿量演化。我们表明，随着后选择强度的增加，这种非厄米哈密顿量可以经历光谱相变。在这种相变的一侧（对于弱后选择），最初混合的密度矩阵始终保持混合状态，并且最初未纠缠的状态发展为体积定律纠缠；另一方面，任意初始状态接近具有低纠缠的唯一纯状态。我们将这种转变与非厄米哈密顿量谱中的一个例外点联系起来，在该点$P吨$对称性自发破缺。我们使用精确的对角化和近似的、分析上易于处理的平均场理论来描述过渡以及混合相后期出现的非平凡稳态；这些方法得出一致的结论。