How to detect entanglement

As we know, entanglement is the most important resource in quantum information, quantum computation, et al. If we have got all the information of the system and can write down its state, we can use many criterions to judge whether the system is entangled or not. The most useful criterion is the “Peres criterion”. But in the laboratory it is very difficult to get all the information of the system. In this limited condition, how can we detect entanglement?

The physicist’s logic is very simple. In principle only Hermite physical quantity is measurable. For example susceptibility is measurable. If we can find some physical quantity that must be fulfilled some condition if the system is separable, we can use it to detect the entanglement. This quantity is called entanglement witness.

To get the condition of entanglement, uncertainty relation and Schwarz inequality should be used together with the definition of the separable state. Most of the witness are the variance of some quantity which could be detected directly. But no witness is good enough to detect all entanglement. For example, it is very difficult to detect the entanglement of the Bell state through entanglement witness. Many new witness will be introduced to improve detection efficient and detect more entangled states.

From ICQO, Hong Kong

I am writing the entrice by using the guest computer of Physics Department, CUHK during the lunch break of the conference.

Honk Kong is a beautiful city and the CUHK is very beautiful, too. The weather is perfect. Unfortunately, I can’t catch up with the lecturers’s English very well. I canot write more for time is limited. I will write an entrice including more details after returning to Xi’an.

Notes on dissipation

How to consider the dissipation in quantum system, especially the cavity QED system? In my research, two different methods were used: master equation and quantum jump.

Let’s consider the main dissipation in the cavity QED system firstly. There are two channels the system lossing its coherence, the spontaneous emission of atoms and the cavity loss. The root of spontaneous emission is the coupling between atoms and the modes other than cavity modes. The state information losses during spontaneous emission. The coupling between cavity field and the atoms vibration located in the cavity wall lead to cavity loss.

The master equation method includes the dissipation via adding spontaneous emission and cavity loss items in the equation. To solve the equation, we should express the equation in the computational basis and solve the matrix equaition. This is not a easy task.

The quantum jump approach bases on the principle of quantum mechanics that the quantum system is probalisitic. During the evolution, for a single atom, it could jump and could not jump. If we focus on the latter condition, we can get the probability that the system doesn’t decay. Conditional Hamiltonian is defined to calculate this probability. This method is suit for the system contains a few atoms and cavity modes.