Over the past decade, classical optical systems with gain or loss, modeled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic states is fundamentally voided by quantum-limited amplifier noise. Here, we show that second-quantized Hermitian Hamiltonians on the Fock space give rise to non-Hermitian effective Hamiltonians that generate the dynamics of corresponding creation and annihilation operators. Using this equivalence between PT-symmetry and symplectic Bogoliubov transformations, we create a quantum optical scheme comprising squeezing, phase-shifters, and beam-splitters for simulating arbitrary non-unitary processes by way of singular value decomposition. In contrast to the post-selection scheme for non-Hermitian quantum simulation, the success probability in this approach is independent of the system size or simulation time and can be efficiently Trotterised similar to a unitary transformation.

中文翻译：

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通过辛变换实现量子非线性光学中的非厄米性

在过去的十年中，人们对由非厄米宇称时间对称哈密顿量建模的具有增益或损耗的经典光学系统进行了深入研究。然而，它们在具有数字分辨光子态的量子域中的适用性从根本上被量子限制放大器噪声所抵消。在这里，我们证明福克空间上的第二量子化埃尔米特哈密顿量会产生非埃尔米特有效哈密顿量，从而生成相应的创建和湮灭算子的动力学。利用 PT 对称性和辛 Bogoliubov 变换之间的等价性，我们创建了一个包含压缩、移相器和分束器的量子光学方案，用于通过奇异值分解来模拟任意非酉过程。与非厄米量子模拟的后选择方案相比，该方法的成功概率与系统尺寸或模拟时间无关，并且可以类似于酉变换那样有效地进行 Trotterized。