Operators

Pieter Kok

Li Hua

Separable operators and PPT operators on a finite dimensional tensor product space are introduced.Then,general forms of separable self-adjoint operators,separable projective operators and separable positive operators are obtained.The relationship between separable operators and PPT operators are proved,and some examples which are PPT operators but not separable operators are given.Lastly,separable maps and PPT maps are introduced and discussed,and it is proved that every separable map maps a PPT operator as a PPT operator.

Dai Yan-wei

In the quantum mechanics,the whole characteristic can be reflected well using the operator.Meanwhile,the mechanical properties can be distilled from the wave function by the operator.When solving or inferring the relation of operators,we not only grasp the significance and property of the related operator,but also understand some basic operational methods of operator.This paper introduces several common operational methods of operator in the quantum mechanics through giving examples.Such as the direct,functional,parameter differential,undetermined operator,integral transform, mathematical induction methods and so on.

Jochen Pade

Jochen Pade

Hailong Shi, Xiao-Hui Wang, Siyuan Liu +3 more

We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence-preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO ⊂ PIO ⊂ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been provided, which indicates that SIO with only two Kraus operators are enough to realize this transformation. The transformation regions of single qubits via CPO and PIO are also given. Our method provides a geometric illustration to analyze single qubit coherence transformations by introducing the Bloch sphere depiction of the transformation regions, and tells us how to construct the corresponding coherence-free operations.