Photon entanglement in the phase-space Q representation of quantum optics

P. Tombesi

Warit Asavanant, Akira Furusawa

Basic concepts of quantum optics are introduced in this chapter. In the beginning, we give a review of the basic quantum mechanics. Then, we perform quantization of an electromagnetic field, which naturally introduces the concept of mode and quadrature. After that, we introduce basic quantum states of light and their phase space representation. Quantum operations in the continuous-variable system and their universality are also explained. To obtain the values of the physical quantities, we have to measure our quantum systems. In the optical continuous-variable system, homodyne measurement and photon number measurement are among the most common measurements that are also discussed here. Finally, we introduce the concept of quantum entanglement, which is one of the central concepts in quantum computation.

Ivan B. Djordjević, Vijay Nafria

In entanglement assisted communications and sensing the optical phase-conjugation (OPC), required before homodyne detection takes place, is typically performed on signal photons on receive side. Unfortunately, in turbulent free-space optical channels, the signal photons can be scattered or absorbed by the channel, and if they reach the receive side they are very weak. Here we propose an entanglement assisted radar technique in which the OPC is performed on bright idler photons instead. By performing the OPC on idler photons on transmit side, while employing adaptive optics and classical homodyne detection on receive side, we experimentally demonstrate that the target detection probability of the proposed entanglement assisted radar over turbulent free-space optical channel is significantly better than that of corresponding classical detection scheme.

David S. Simon, Gregg S. Jaeger, Alexander V. Sergienko

Liyun Hu, Hong-Yi Fan

We construct a generalized phase-space representation (GPSR) based on the idea of Einstein-Podolsky-Rosen quantum entanglement, i.e., we generalize the Torres-Vega-Frederick phase-space representation to the entangled case, which is characteristic of the features when two particles' relative coordinate, total momentum operators, and their conjugative variables, respectively, operate on the GPSR. This representation is complete and nonorthogonal. The Weyl-ordered form of the density operator of GPSR is derived, and its identification with the generalized Husimi operator is recognized, which clearly exhibit its statistical behavior. The minimum uncertainty relation obeyed by the GPSR is also demonstrated.

Sang-Kyung Choi, Hee Su Park