Quantum deleting and cloning in a pseudo-unitary system

TL;DR

This paper explores how pseudo-unitary systems can enable perfect deleting and cloning of nonorthogonal quantum states, challenging traditional quantum no-deleting and no-cloning theorems, with practical simulation considerations.

Contribution

It introduces a pseudo-Hermitian Hamiltonian allowing perfect deleting and cloning of nonorthogonal states, and discusses simulation via post-selection in conventional quantum mechanics.

Findings

Pseudo-unitary operators enable perfect deletion and cloning of certain states.

Simulation success probabilities are less than one due to post-selection limitations.

Quantum no-deleting and no-cloning theorems are upheld in practical simulations.

Abstract

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.