Title:
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Quantum correlations in multi-photon quantum walks
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Quantum particles show a distinct behaviour compared to classical particles. The
fundamental principles of superposition and entanglement lead to interference effects,
which often seem to contradict common sense trained by classical physics.
Within the emerging field of quantum information and computation techniques for
harnessing these quantum interference effects for information processing tasks have
been developed.
A complex interference phenomenon, which is at the heart of theoretical and
experimental quantum information, is quantum walks. It describes the movement of
quantum mechanical particles within a discretised space and finds applications in
designing quantum algorithms and for implementing quantum simulations.
This thesis explores multi-photon interference of identical and entangled particles
in physically implemented quantum walk structures. In particular, we realise
continuous-time quantum walks, using single photons propagating in integrated
waveguide arrays. Here, the evolution is given by the continuous evanescent coupling
of the photons between neighbouring waveguides.
We demonstrate two-photon quantum walks on a one-dimensional line, where we
can observe the time evolution by measuring the output distribution of waveguide arrays
with varied lengths. Within this work, we investigate boundary conditions and
coherence of the evolution. Additional to this, we employ waveguides, laser-written
in glass substrate, implementing a quantum walk on a two-dimensional graph structure.
We show quantum interference effects between two photons, which are unique
to this two-dimensional structure. In a third experiment, we measure the quantum
walk of up to five photons. We compare the output statistics of this structured
unitary with the output of a random circuit and we construct a metric for verifying
quantum interference. Furthermore, we show, that quantum correlations of
entangled particles prevail in a noisy environment and .allow the construction of an
entanglement witness. Finally, we utilise entanglement for quantum statistics simulations.
Here, we can simulate quantum statistics effects, such as Pauli-exclusion.
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