The Role of Entanglement in Quantum Communication, and Analysis of the Detection Loophole

Entanglement is a feature at the heart of quantum information. Its enablement of
unusual correlations between particles drives a new wave of communication and computation. This thesis explores some of the ways in which the tools for studying entanglement
can be used to quantify the transmission of quantum information, and compares the use
of different techniques.
We begin this thesis by expanding the technique of teleportation simulation, which adds
noise to the entangled resource state to mimic channel effects. By introducing classical
noise in the communication step, we show it is possible to simulate more than just Pauli
channels using teleportation. This new class is characterised, and studied in detail for a
particular resource state, leading to a family of simulable channels named “Pauli-Damping
channels” whose properties are analysed.
Also introduced are a new family of quantum states, “phase Werner” states, whose
entanglement properties relate to the interesting conjecture of bound entangled states
with a negative partial transpose. Holevo-Werner channels, to which these states are
connected, are shown to be teleportation covariant. We exploit this to present several
interesting results, including the optimal estimation of the channel-defining parameter.
The minimal binary-discrimination error for Holevo-Werner channels is bounded for the
first time with the analytical form of the quantum Chernoff bound. We also consider
the secret key capacity of these channels, showing how different entanglement measures
provide a better upper bound for different regions of these channels.
Finally, a method for generating new Bell inequalities is presented, exploiting nonphysical probability distributions to obtain new inequalities. Tens of thousands of new
inequivalent inequalities are generated, and their usefulness in closing the detection loophole for imperfect detectors is examined, with comparison to the current optimal construction. Two candidate Bell inequalities which may equal or beat the best construction are
presented.