We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essen...We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essentially a direct analog of having the Minkowski spacetime with an indefinite signature generalizing the metric geometry of the Newtonian space. In fact, the explicit physics setting we have in mind is exactly a Lorentz covariant formulation of quantum mechanics, which has been discussed in the literature for over half a century yet without a nice full picture. From the point of view of the Lorentz symmetry, indefiniteness of the norm for a Minkowski vector may be the exact correspondence of the indefiniteness of the norm for a quantum state vector on the relevant Hilbert space. That, of course, poses a challenge to the usual requirement of unitarity. The related issues will be addressed.展开更多
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 inve...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.展开更多
文摘We present the theoretical considerations for the case of looking into a generalization of quantum theory corresponding to having an inner product with an indefinite signature on the Hilbert space. The latter is essentially a direct analog of having the Minkowski spacetime with an indefinite signature generalizing the metric geometry of the Newtonian space. In fact, the explicit physics setting we have in mind is exactly a Lorentz covariant formulation of quantum mechanics, which has been discussed in the literature for over half a century yet without a nice full picture. From the point of view of the Lorentz symmetry, indefiniteness of the norm for a Minkowski vector may be the exact correspondence of the indefiniteness of the norm for a quantum state vector on the relevant Hilbert space. That, of course, poses a challenge to the usual requirement of unitarity. The related issues will be addressed.
基金This work was funded by the National Natural Science Foundation of China(Grant Nos.11734015,11474049,and 11674056)the K.C.Wong Magna Fund in Ningbo University,the financial support from Research Grants Council of Hong Kong(RGC,Hong Kong)(Grant No.538213)+1 种基金M.G.was supported by the National Youth Thousand Talents Program(Grant No.KJ2030000001)the USTC start-up funding(Grant No.KY2030000053).
文摘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.
