We study the transition of a quantum system S from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system E coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of E modelled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of E strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing S vanish sharply. Introduction: Nowadays quantum -classical transitions described by a reduction from a pure state to a mixture [1, 2] renew interests in many areas of physics, mainly due to the importance of quantum measurement and decoherence problem in quantum computing. To study this transition, some exactly-solvable models were proposed for a system coupled to the macroscopic [3,4,5] or classical [6,7] surrounding systems. Relevantly, in association with the quantum -classical transition in quantum chaos, the concept of Loschmidt echo (LE) from NMR experiments was introduced to describe the hypersensitivity of the time evolution to the perturbations experienced by the surrounding system [8,9]. In this letter, by a concrete example, we will show how quantum phase transition (QPT) [10] of the surrounding system can also sensitively affect the decay of its own LE, which means a dynamic reduction of its coupled system from pure state to a mixed one. Here, we note that a QPT effect has been explored for the Dicke model at the transition from quasi-integrable to quantum chaotic phases [11].

For the two-mode exciton system formed by the quasi-spin-wave collective excitation of many Lambda atoms fixed at the lattice sites of a crystal, we discover a dynamical symmetry depicted by the semidirect product algebra SU2( multiply sign in circle) h(2) in the large N limit with low excitations. With the help of the spectral generating algebra method, we obtain a larger class of exact zero-eigenvalue states adiabatically interpolating between the initial state of photon-type and the final state of quasi-spin-wave exciton-type. The conditions for the adiabatic passage of dark states are shown to be valid, even with the presence of the level degeneracy. These theoretical results can lead to the proposal of a new protocol for implementing quantum memory robust against quantum decoherence.

The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of environment on quantum computation is probed on the basis of its analogy to the problem of wave function collapse in quantum measurement.Techniques from the Hepp-Colemen approach and its generalization are used to deal with decoherence problems in quantum computation including dynamic mechanism of decoherence , quantum error avoiding tricks and calculation of decoherence time.

In a close form without referring the time-dependent Hamiltonian to the total system, a consistent approach for quantum measurement is proposed based on Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516]. An exactly-solvable model based on the intracavity system is dealt with in details to demonstrate the central idea in our approach: by peeling off one collective variable of the measuring apparatus from its many degrees of freedom, as the pointer of the apparatus, the collective variable de-couples with the internal environment formed by the effective internal variables, but still interacts with the measured system to form a triple entanglement among the measured system, the pointer and the internal environment. As another mechanism to cause decoherence , the uncertainty of relative phase and its many-particle amplification can be summed up to an ideal entanglement or an Shmidt decomposition with respect to the preferred basis.