In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum deleting and cloning in a pseudo-unitary system. We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system. By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian, we show that it is possible to delete and clone a class of two different and nonorthogonal states, and it can be generalized to arbitrary two different and nonorthogonal pure qubit states. Furthermore, state discrimination, which is strongly related to quantum no-cloning theorem, is also discussed. Last but not least, we simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection, and obtain the success probability of simulations. Pseudo-unitary operators are implemented with a limited efficiency due to the post-selections. Thus, the success probabilities of deleting and cloning in the simulation by conventional quantum mechanics are less than unity, which maintain the quantum no-deleting and no-cloning theorems.

在传统的量子力学中，量子无删除定理和无克隆定理表明，两个不同的非正交状态不能分别被确定性地删除和克隆。在这里，我们研究伪deleting系统中的量子删除和克隆。我们首先提出一个在两个量子位系统中具有真实特征值的伪Hermitian哈密顿量。通过使用从该伪-Hermitian哈密顿量生成的伪-算子，我们表明可以删除和克隆一类两个不同且非正交的状态，并且可以将其推广到任意两个不同且非正交的纯量子位状态。此外，还讨论了与量子无克隆定理密切相关的状态判别。最后但并非最不重要的，我们利用后选择模拟了传统量子力学中的伪unit算子，并获得了模拟的成功概率。由于后选择，伪-运算符的实现效率有限。因此，通过传统的量子力学在模拟中进行删除和克隆的成功概率小于1，从而保持了量子无删除和无克隆定理。