Quantum deleting and cloning in a pseudo-unitary system
arXiv:2103.15353 · doi:10.1007/s11467-021-1063-z
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.
arXiv comment6 pages
References in corpus (24)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Complex Extension of Quantum Mechanics
- Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
- PT-Symmetric Quantum Mechanics
- PT-symmetry breaking and laser-absorber modes in optical scattering systems
- Visualization of Branch Points in PT-Symmetric Waveguides
- Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
- Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
- Quantum cloning
- Reversing the Pump-Dependence of a Laser at an Exceptional Point
- Pump-induced Exceptional Points in Lasers
- Physical realization of -symmetric potential scattering in a planar slab waveguide
- Probabilistic cloning and identification of linearly independent quantum states
- Faster than Hermitian Quantum Mechanics
- Impossibility of deleting an unknown quantum state
- The Naimark dilated PT-symmetric brachistochrone
- Local PT symmetry violates the no-signaling principle
- Quantum Cloning Machines and the Applications
- Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
- Consistency of PT-symmetric quantum mechanics
- The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
- PT-symmetric quantum state discrimination
- Is PT-symmetric quantum theory false as a fundamental theory?