Quantum deleting and cloning in a pseudo-unitary system
Yu-Cheng Chen1, Ming Gong2, Peng Xue3, Hai-Dong Yuan4, Cheng-Jie Zhang1,5()
1. School of Physical Science and Technology, Ningbo University, Ningbo 315211, China 2. Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China 3. Beijing Computational Science Research Center, Beijing 100084, China 4. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China 5. School of Physical Science and Technology, Soochow University, Suzhou 215006, China
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.
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