In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.

中文翻译：

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通过分束器上的条件测量生成的有限维量子态

在这项工作中，通过对分束器（BS）进行条件测量，对量子剪刀（QS）装置的基本思想进行了一些修改，以生成有限维的量子态。事实证明，取决于BS的传输系数，具有两个单光子输入和两个单光子检测的QS器件仅仅是由真空状态，单光子状态和双光子状态组成的投影算子。作为最一般的示例，我们将压缩的相干状态视为输入状态，并导出输出状态的解析表达式。通过平均光子数，强度增益和维格纳函数详细分析了其非经典特性。此外，我们将此技术扩展到了两模式压缩真空状态（TMSVS）。结果状态就是广义的贝尔状态，仅包含双真空，双单光子和双双光子两个分量，它们的纠缠特性由冯·诺依曼熵和爱因斯坦·波多尔斯基—罗森相关性定量。结果表明，在一定的压缩参数和透射率范围内，截断的TMSVS的纠缠比TMSVS的纠缠强。