| Abstract: | Quantum information has been drawing a wealth of research in recent years, shedding light on questions at the heart of quantum mechanics, as well as advancing fields such as complexity theory, cryptography, key distribution, physics and chemistry. A key ingredient to advancement in this field is the ability to characterize quantum states from measurements, through a process called Quantum State Tomography (QST). However, QST is resource consuming, in terms of the number of measurements required, the complexity of the measurements and the experimental effort needed. Thus, full QST is impractical already for rather small systems. This seminar will present several topics that deal with schemes for the recovery of photonic quantum states from measurements. The schemes we propose are much simpler than QST and aim to overcome drawbacks of QST. The simplification relies the ability to recover the quantum states from incomplete measurements. To overcome the missing information, we employ general prior knowledge about the quantum state we wish to recover, namely, that it can be represented compactly (sparsely) in some basis. The sparse representation enables a variety of tools, as well as inspires modifications to the measurement process, yielding state recovery from partial information. For example, we show how three-photon states can be recovered from two-fold correlation measurements, and how states can be recovered efficiently from measurements of a single observable, in a single experimental setup. |
