טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentCaspi Dikla
SubjectStructure Based State Recovery of Quantum Light
and Open Quantum Systems
DepartmentDepartment of Physics
Supervisor ? 18? Mordechai Segev


Abstract

Quantum information has been drawing a wealth of research recently, shedding light on questions at the heart of quantum mechanics, as well as advancing topics in physics and related fields. A key ingredient in the 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 required number of measurements and the experimental effort needed. Thus, full QST is impractical already for rather small systems.

This thesis presents several schemes for the recovery of photonic quantum states from measurements. The schemes we propose are simpler than QST and aim to overcome some of its drawbacks. The simplification relies on the ability to recover states from incomplete measurements. To overcome the missing information, we employ general prior knowledge about the sought quantum state, namely, that it can be represented compactly (sparsely) in some basis. The prior knowledge should be general enough to be applicable to a wide variety of states in interesting physical systems, however, it should be strong enough to allow recovery from missing information. In particular, we use the fact that often, quantum states of interest are close to pure. The sparse representation enables a variety of tools, as well as inspires modifications to the measurement process to yield state recovery.

First, this thesis investigates the problem of recovering multi-photon states from measurements of low-order correlations. To characterize multi-photon states with a fixed (or bounded) photon number, multi-photon correlations are needed. However, high-order correlations are hard to measure, as the rate of high-order coincidences decreases very fast when the correlation order increases. This results in a poor signal-to-noise ratio. We show numerically that using the generic prior knowledge - that the sought state has structure, three-photon states can be recovered from measurements of two-fold correlations.

This thesis also studies the problem of recovering quantum states from measurements in a single measurement setting. QST, formulated in terms of physical observables, requires a tomographically complete set of observables. Often, different observables require changing the experimental setup, prolonging the measurement process, and hampering the assumptions often made about the noise, such as stationarity. Thus, it is beneficial to reduce the number of observables and setups needed. We propose a way to recover quantum states by measuring a single observable, in a single experimental setup. The same scheme is also used to recover states with a fixed photon number, with ordinary click detectors. We also propose a simple method to assess whether enough measurements have been taken, based on sensitivity to a small reduction in the number of measurements.

The thesis also studies the propagation of single photons inside a coherent lossy beamsplitter, accompanying an experiment performed by collaborators.

Finally, this thesis also investigates the topological protection of biphoton states in a nonlinear four-wave mixing medium, which is a 1D SSH lattice.