We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in 2 × 2 × N quantum systems) is separable, we s...We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in 2 × 2 × N quantum systems) is separable, we show that some quantity in relationto Hermitian matrix is positive.展开更多
The general expression with the physical significance and positive-definite condition of the eigenvalues of 4 × 4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability con...The general expression with the physical significance and positive-definite condition of the eigenvalues of 4 × 4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability condition for an arbitrary state of two qubits is then given and its operational feature is enhanced. Furthermore, we discuss some applications to the calculation of the entanglement, the upper bound of the entanglement, and a model of the transfer of entanglement in a qubit chain with noise.展开更多
The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potenti...The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V1 (x) = (ix)(2n+1)/m and general polynomial potential V2(x) = x2M + ib1x2M-1 + b2x2M-2 +... + ib2M-1x. The level spacing distribution of V1 has two forms. When 2n + 1 - 2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n + 1 - 2m is negative.The PT symmetry of this system is spontaneously broken as 2n + 1 - 2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V2 assumes an increasing power function when order of the polynomial is greater than two.展开更多
It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its des...It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.展开更多
Active Contour Model or Snake model is an efficient method by which the users can extract the object contour of Region Of Interest （ROI）. In this paper, we present an improved method combining Hermite splines curve ...Active Contour Model or Snake model is an efficient method by which the users can extract the object contour of Region Of Interest （ROI）. In this paper, we present an improved method combining Hermite splines curve and Snake model that can be used as a tool for fast and intuitive contour extraction. We choose Hermite splines curve as a basic function of Snake contour curve and present its energy function. The optimization of energy minimization is performed hy Dynamic Programming technique. The validation results are presented, comparing the traditional Snake model and the HSCM, showing the similar performance of the latter. We can find that HSCM can overcome the non-convex constraints efficiently. Several medical images applications illustrate that Hermite Splines Contour Model （HSCM） is more efficient than traditional Snake model.展开更多
Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices w...Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.展开更多
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There a...To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.展开更多
文摘We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in 2 × 2 × N quantum systems) is separable, we show that some quantity in relationto Hermitian matrix is positive.
文摘The general expression with the physical significance and positive-definite condition of the eigenvalues of 4 × 4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability condition for an arbitrary state of two qubits is then given and its operational feature is enhanced. Furthermore, we discuss some applications to the calculation of the entanglement, the upper bound of the entanglement, and a model of the transfer of entanglement in a qubit chain with noise.
文摘The correspondence between quantum level spacing distribu tions and classical motion of 1-D P T symmetric non-Hermitian systems is investigated using two PT symmetric complex potentials: complex rational power potential V1 (x) = (ix)(2n+1)/m and general polynomial potential V2(x) = x2M + ib1x2M-1 + b2x2M-2 +... + ib2M-1x. The level spacing distribution of V1 has two forms. When 2n + 1 - 2m is positive, the level spacing distribution of real eigen values assumes a decreasing power function, while it behaves as an increasing power function when 2n + 1 - 2m is negative.The PT symmetry of this system is spontaneously broken as 2n + 1 - 2m becomes negative. This change manifests itself in classical mechanics as it is found by Bender et al. However, it was found that the change in the form of level spacing distribution mentioned above is not due to the spontaneous breaking down of PT symmetry. Level spacing distribution of V2 assumes an increasing power function when order of the polynomial is greater than two.
基金Supported by the National Natural Science Foundation of China (No.60403004)the Outstanding Youth Foundation of China (No.0612000500)
文摘It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.
文摘Active Contour Model or Snake model is an efficient method by which the users can extract the object contour of Region Of Interest （ROI）. In this paper, we present an improved method combining Hermite splines curve and Snake model that can be used as a tool for fast and intuitive contour extraction. We choose Hermite splines curve as a basic function of Snake contour curve and present its energy function. The optimization of energy minimization is performed hy Dynamic Programming technique. The validation results are presented, comparing the traditional Snake model and the HSCM, showing the similar performance of the latter. We can find that HSCM can overcome the non-convex constraints efficiently. Several medical images applications illustrate that Hermite Splines Contour Model （HSCM） is more efficient than traditional Snake model.
文摘Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.
文摘To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.
