null

We review some results on analytical computations of the measures for quantum entanglement: entanglement of formation and concurrence. We introduce some estimations of the lower bounds for the entanglement of formation in bipartite mixed states, and of lower bounds for the concurrence in bipartite and tripartite systems. The results on lower bounds for the concurrence are also generalized to arbitrary multipartite systems.

We investigate the decoherence control coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum computation. Especially, we find that deriving optimal control using the Pontryagin maximum principle, the decoherence can be suppressed even in high-temperature reservoirs. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under ?_c ? ?₀ condition, here ?₀ is the characteristic frequency of the quantum system of interest, and ?_c the cut-off frequency of Ohmic reservoir. It implies that designing some engineered reservoirs with the controlled coupling and state of the environment can slow down the decoherence rate and delay the decoherence time. Moreover, we compared the non-Markovian optimal decoherence control with the Markovian one and find that with non-Markovian the engineered artificial reservoirs are better than the Markovian approximate in controlling the decoherence of open, dissipative quantum systems.

Grover presented the Phase-?/3 search by replacing the selective inversions by selective phase shifts of ?/3. In this paper, we review and discuss the fixed-point search with general but equal phase shifts and the fixed-point search with general but different phase shifts.

Quantum error correcting codes are indispensable for quantum information processing and quantum computation. In 1995 and 1996, Shor and Steane gave first several examples of quantum codes from classical error correcting codes. The construction of efficient quantum codes is now an active multi-discipline research field. In this paper we review the known several constructions of quantum codes and present some examples.

In this article, we review the recent development of controlled teleportation which can be used for sharing quantum information and has important applications in remote quantum computation. We introduce the principles of a couple of controlled teleportation schemes with maximally entangled quantum channels and those with pure entangled quantum channels (non-maximally entangled states). The schemes based on maximally entangled states have the advantage of having maximal efficiency although there are differences in their implementations in experiment. In the controlled teleportation schemes using non-maximally entangled states as the quantum channels, the receiver can reconstruct the originally unknown state by adding an auxiliary particle and performing a unitary evolution. No matter what the unknown state is (a single qubit state or an m-qudit state), the auxiliary particle required is only a two-level quantum system.

After giving a bird’s view of some existing quantum programming languages, this paper reports the recent results made by the quantum computation group of the State Key Laboratory for Novel Software Technology and the Department of Computer Science and Technology at Nanjing University, i.e., the quantum programming languages NDQJava, NDQFP and their processing systems.

In this article, we make a review on the development of a newly proposed quantum computer, duality computer, or the duality quantum computer and the duality mode of quantum computers. The duality computer is based on the particle-wave duality principle of quantum mechanics. Compared to an ordinary quantum computer, the duality quantum computer is a quantum computer on the move and passing through a multi-slit. It offers more computing operations than is possible with an ordinary quantum computer. The most two distinct operations are: the quantum division operation and the quantum combiner operation. The division operation divides the wave function of a quantum computer into many attenuated, and identical parts. The combiner operation combines the wave functions in different parts into a single part. The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer. The main structure of duality quantum computer and duality mode, the duality mode, their mathematical description and algorithm designs are reviewed.

In this article we make a review on the usefulness of probabilistically cloning and present examples of quantum computation tasks for which quantum cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, one needs to distribute quantum information contained in states about which we have some partial information. To perform quantum computations, one uses state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation. And we discuss the achievable efficiencies and the efficient quantum logic network for probabilistic cloning the quantum states used in implementing quantum computation tasks for which cloning provides enhancement in performance.

In this article, we review the relationship between Bell inequality and its associated polytopes and introduce a method to extend Bell inequalities to more parties. According to this method, the Bell inequality in n parties can be extended to n + 1 parties. Such generalization is nontrivial in that there is stronger violation for new inequalities.

Quantum automata, as theoretical models of quantum computers, include quantum finite automata (QFA), quantum sequential machines (QSM), quantum pushdown automata (QPDA), quantum Turing machines (QTM), quantum cellular automata (QCA), and the others, for example, automata theory based on quantum logic (orthomodular lattice-valued automata). In this paper, we try to outline a basic progress in the research on these models, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata. Also, other models closely relative to them are mentioned. In particular, based on the existing results in the literature, we finally address a number of problems to be studied in future.