Stationary entanglement and nonlocality of two qubits or qutrits collectively interacting with the thermal environment: The role of Bell singlet state

Abstract

We investigate the stationary entanglement and stationary nonlocality of two qubits collectively interacting with a common thermal environment. We assume two qubits are initially in Werner state or Werner-like state, and find that thermal environment can make two qubits become stationary nonlocality. The analytical relations among average thermal photon number of the environment, entanglement and nonlocality of two qubits are given in details. It is shown that the fraction of Bell singlet state plays a key role in the phenomenon that the common thermal reservoir can enhance the entanglement of two qubits. Moreover, we find that the collective decay of two qubits in a thermal reservoir at zero-temperature can generate a stationary maximally entangled mixed state if only the fraction of Bell singlet state in the initial state is not smaller than 2/3. It provides us a feasible way to prepare the maximally entangled mixed state in various physical systems such as the trapped ions, quantum dots or Josephson Junctions. For the case in which two qutrits collectively coupled with the thermal reservoir at zero-temperature, we find that the collective decay can induce the entanglement of two qutrits initially in the maximally mixed state. The collective decay of two qutrits can also induce distillable entanglement from the initial conjectured negative partial transpose bound entangled states.