Abstract
Quantum information science is a flourishing field of research, despite its relative nascency.A helpful perspective is to focus on specific features and properties of quantum mechanics, and
consider their role as resources for certain scenarios or tasks.
In this thesis, we introduce several novel concepts and definitions by building on ideas
present in the existing literature. Specifically we explore research questions relating to quantum
steering, measurement incompatibility, coherence, and aspects of entanglement (such as highdimensionality
and the multipartite scenario).
Firstly in Chapter 2, taking inspiration from quantum nonlocality in networks, we consider
allowing some of the parties to be trusted, which leads us to a natural notion of quantum network
steering. We are able to characterise several scenarios for which only classical correlations can
arise, and we also provide examples of when network steering can be exhibited, including an
example that appears unique to networks and does not rely on existing steering results.
In Chapter 3, we introduce a notion of dimensionality for sets of quantum measurements,
which can also be understood as a form of compression, or as a kind of Schmidt number
for measurement incompatibility. We discuss and prove several links to high-dimensional
quantum steering, and provide connections between several interesting channels and states via
channel-state duality.
We then change gears somewhat, and in Chapter 4 we consider the role of coherence in
gadget-based approaches to quantum computation. We construct a general framework for
quantum computation involving ‘free’ operations acting on some resourceful state, and prove
a no-go result, stating that some coherence must be present in the operations to achieve
computational universality: one cannot place this resource in a supplementary state.
Finally, in Chapter 5 we prove a lower bound on the number of copies needed to determine
whether a pure multipartite quantum state is either product across some bipartition, or is far
away from having this property. Our lower bound is tight compared to known upper bounds up
to a logarithmic factor.
In a broad sense, this thesis aims to display the power of quantum resources and to unearth
interesting connections between seemingly different notions in quantum information science.
The results presented serve as a testament to the variety and richness of research in this field,
and expose the exciting realm of future research topics and questions to explore.
| Date of Award | 1 Oct 2024 |
|---|---|
| Original language | English |
| Awarding Institution |
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| Supervisor | Paul Skrzypczyk (Supervisor) & Noah Linden (Supervisor) |