arXiv subjects
Publications and source records attributed to Li-Xiang Cen.
The effects of dissipation on a holonomic quantum computation scheme are analyzed within the quantum-jump approach. We extend to the non-Abelian case the refocusing strategies formerly introduced for (Abelian) geometric computation. We show how double loop symmetrization schemes allow one to get rid of the unwanted influence of dissipation in the no-jump trajectory.
We propose a non-adiabatic scheme for geometric quantum computation with trapped ions. By making use of the Aharonov-Anandan phase, the proposed scheme not only preserves the globally geometric nature in quantum computation, but also provides the advantage of non-adiabaticity that overcomes the problem of slow evolution in the existing adiabatic schemes. Moreover, the present scheme requires only two atomic levels in each ion, making it an appealing candidate for quantum computation.
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo orthonormalized. The two-to-one homomorphism is then established for the group $SL(2,C)\otimes SL(2,C)$ onto the $SO(4,C)$. It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.
Time-resolved Faraday rotation spectroscopy is currently exploited as a powerful technique to probe spin dynamics in semiconductors. We propose here an all-optical approach to geometrically manipulate electron spin and to detect the geometric phase by this type of extremely sensitive experiment. The global nature of the geometric phase can make the quantum manipulation more stable, which may find interesting application in quantum devices.
The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The result obtained is universal for arbitrary entangled two-qubit states and it discloses that the corresponding local filter is not unique for density matrices with rank $n=2$ and can be exclusively determined for that with $n=3$ and 4. As illustrations, a four-parameters family of mixed states are explored, the local filter as well as the transformation probability are given explicitly, which verify the validity of the general result.
We present a general algorithm to achieve local operators which can produce the GHZ state for an arbitrary given three-qubit state. Thus the distillation process of the state can be realized optimally. The algorithm is shown to be sufficient for the three-qubit state on account of the fact that any state for which this distillation algorithm is invalid cannot be distilled to the GHZ state by any local actions. Moreover, an analytical result of distillation operations is achieved for the general state of three qubits.