The quantum effects for a physical system can be described by the set ε(H) of positive operators on a complex Hilbert space Hthat are bounded above by the identity operator Ⅰ. The infimum problem of Hilbert space ef...The quantum effects for a physical system can be described by the set ε(H) of positive operators on a complex Hilbert space Hthat are bounded above by the identity operator Ⅰ. The infimum problem of Hilbert space effects is to find under what condition the infimum A∧B exists for two quantum effects A and B ∈ε(H). The problem has been studied in different contexts by R. Kadison, S. Gudder, M. Moreland, and T. Ando. In this note, using the method of the spectral theory of operators, we give a complete answer of the infimum problem. The characterizations of the existence of infimum A ∧ B for two effects A, B ∈ε(H) are established.展开更多
By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper...By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10571113).
文摘The quantum effects for a physical system can be described by the set ε(H) of positive operators on a complex Hilbert space Hthat are bounded above by the identity operator Ⅰ. The infimum problem of Hilbert space effects is to find under what condition the infimum A∧B exists for two quantum effects A and B ∈ε(H). The problem has been studied in different contexts by R. Kadison, S. Gudder, M. Moreland, and T. Ando. In this note, using the method of the spectral theory of operators, we give a complete answer of the infimum problem. The characterizations of the existence of infimum A ∧ B for two effects A, B ∈ε(H) are established.
基金partially supported by National Natural Science Foundation of China (Grant Nos. 10761006, 11161034)
文摘By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role.
