title: Verifying Entanglement of Constrained Bipartite Quantum Systems
Creators: name: Jones, Steven
Publisher: name: Griffith University
Year: 2009
Subjects: subject: Constrained Bipartite Quantum Systems
subject: Microscopic physical systems
subject: quantum technologies
subject: quantum resources
subject: superselection

description: Microscopic physical systems requiring a quantum description are increasingly being harnessed to develop useful technologies. The appeal of such an approach lies in the fact that quantum systems possess inherently different properties from those observed on a macroscopic scale. Uniquely quantum phenomena, such as entanglement, offer new tools for performing experimental tasks. For instance, the use of quantum systems for implementing cryptographic protocols and performing computation has caused significant excitement in recent years as it seems likely that the quantum approach offers an advantage over purely classical implementations. The development of quantum technologies leads to the concept of quantum resources. One key quantum resource that lies at the heart of the divergence between quantum and classical descriptions is that of entanglement. However, for entanglement to act as a resource, it must be possible for the parties (we will restrict ourselves to only two) sharing the entanglement to verify its presence. This may seem like a simple task, however, verifying the properties of quantum systems can be nontrivial. To make matters more complicated, there are often constraints under which the parties sharing the quantum systems find themselves which further restrict the ability of the quantum systems to act as a resource. One family of constraints arises when the two parties are dealing with quantum systems which have properties constrained by a conservation law, or some other constraint which limits knowledge of the properties of the local subsystems. These constraints can be expressed using the well studied formalism of superselection rules. When a superselection rule applies to quantum systems it can be ambiguous as to whether entanglement survives between the systems. This thesis considers a situation that arises naturally in a nuclear magnetic resonance experiment where two parties share many copies of identical quantum systems. In this case a superselection rule associated with the finite symmetric group applies due to the indistinguishability of the systems. The concept of a reference frame for the symmetric group is used to alleviate the effect of the superselection rule and demonstrate when entanglement survives despite the constraint of indistinguishability. In addition to this, a situation which goes beyond the superselection formalism is considered, one where the operations performable by the two parties are further constrained. It is shown that despite this stronger constraint, it is still possible in principle to verify the existence of entanglement experimentally as demonstrated by the violation of a Bell inequality. Methods for verifying the presence of entanglement can also prove useful in characterising the properties of entangled quantum systems. Such characterisation may offer insight into the possible advantages offered by quantum systems over their classical counterparts. It becomes possible to more accurately characterise entangled systems by considering a conceptual constraint under which the two parties may find themselves. This is the situation that arises when one of the parties, say Bob, distrusts the other, Alice. In this situation, Alice can only convince Bob of the presence of their entanglement if the entangled system they share possesses a certain property. We term this property steerability, after Schrödinger’s term “steering” [Proc. Camb. Phil. Soc. 31, 553 (1935)] for the Einstein-Podolsky-Rosen effect. This thesis offers a rigorous characterisation of steering in a quantum information context and probes a number of questions relating to this property. First, a number of examples are presented which demonstrate state steerability which is a uniquely quantum property possessed by certain entangled states. Second, the task of experimentally detecting steerability, and thus entanglement, is addressed through the introduction of steerability criteria. Finally two more detailed examples are explored which illustrate various aspects of the measurement dependence of steerability in realistic experiments.