Abstract:
Quantum optical interferometry has played a crucial role in precision measurements
and quantum sensing, which laid the foundation of quantum metrology the science
of precision measurements using the laws of quantum mechanics. The precision of any
measurement may be limited by experimental human error and/or ingenuity of measuring
apparatus. However, beyond these limitations quantum mechanics imposes a fundamental
restriction on metrology which can be expressed by Heisenberg Uncertainty
principle. Fortunately, on the other hand, solution to this quantum-induced limitation
is also provided by quantum theory using some non-classical concepts. Hence, quantum
metrology deals with techniques to improve the measurement precision beyond
the limit set by standard quantum uctuations. In many physical situations, precision
measurement process can be reduced to detection of a small phase shift by using optical
interferometric set up.
This thesis is focused on studying the quantum optical phase-estimation and exploring
the fundamental bounds on its ultimate precision in the perspective of classical and
quantum measurement theories. Using the notion of Fisher information entropy, we
nd the so-called Cramér Rao bounds on optical phase-estimation while using classical
as well as quantum probes at our optical set up. We show that by using classical probe
as initial state, the estimation error is estimated at the best as 1=
p
n. This limit
is known as Short Noise Limit (SNL). Interestingly, it is shown that using quantum
probes the ultimate precision limit surpasses SNL and approaches the value as 1= n,
which is known as Heisenberg-limit. It is important to note that in the Heisenberglimited
phase-estimation, the accuracy is enhanced by a factor of
p
n with respect to
SNL.
