# Design, analysis and implementation of advanced quantum communication protocols

**Abstract** :

In this thesis we focus on designing protocols for quantum information processing tasks
that can be implemented with current photonic technologies. We start by providing the first
example of a communication model and a distributed task for which there exists a realistic
quantum protocol asymptotically more efficient than any classical protocol, both in terms
of communication and information resources. To this end, we extend the recently proposed
coherent state mapping for quantum communication protocols, study the use of coherent
state fingerprints over multiple channels and show their role in the design of an efficient
quantum protocol for estimating the Euclidean distance between two real vectors within a
constant factor.
In the second part of the thesis, we propose a new problem in one-way communication
model, Sampling Matching problem, for which there exists an exponential gap between
a realistic quantum protocol and any randomized classical protocol within bounded error.
We implement this problem using attenuated coherent states and linear optics, and show an
advantage in using quantum resources from very low input sizes to the problem. This new
proposal is a far simplified alternative to the previous problems in one-way communication
model due to it requiring O(1) linear optical elements for implementation. This facilitates
the implementation of the quantum protocol for arbitrarily large input sizes.
Then we introduce a private-key quantum money-scheme with the verification protocol
based on the Sampling Matching scheme. We look at the scheme when the Bank prepares
notes as single photon superposition states. The features of our scheme include single-round
classical interaction with the Bank, linear note re-usability, robustness against experimental
imperfection, and an unconditional security against an adversary trying to forge the Bank note.
We then follow up this work by proposing a practical quantum money-scheme when the Bank
prepares notes as attenuated coherent states. This is an experimentally motivated framework
which utilises the advantage offered by the Sampling Matching verification protocol that it
requires only O(1) linear optical elements for implementation.
Finally we introduce a programmable device whose input states control the the measure-
ment operation. In particular, our device is the generalised Sylvester-Hadamard operation to
discriminate two unknown coherent states in the setting of a single copy of one state (test
state), and M −1 copies of the other state (reference state). Our distinguishing scheme
involves M linear optics components (50/50 beam splitters), and M −1 single photon thresh-
old detectors. We show that our setting strictly improves the soundness in discriminating two
coherent states compared to the setting when one is provided only a single copy of the two
states.