The Roles of Causal Propagator in Relativistic Quantum Information

Abstract

This thesis focuses on the roles of causal propagator — the expectation value of the field commutator — in relativistic quantum information. Consider two observers Alice and Bob, each carrying a two-level quantum system (“qubit”) interacting with a common relativistic quantum field environment in spacetime. Since the interaction occurs for a finite duration and has a finite spatial extent, we can think of Alice and Bob’s qubits as being essentially localized in spacetime. We say that Alice and Bob can signal or communicate to one another via the field if the protocol they use depends on the field commutator evaluated around Alice’s and Bob’s interaction regions. The main tool we use to deal with signaling issues is the so-called Unruh-DeWitt particle detector model.

The main content of the thesis is organized into four chapters (Chapter 4-7). Chapter 4 and 5 are concerned with the entanglement harvesting protocol, where Alice and Bob attempt to extract vacuum entanglement from the relativistic environment by locally coupling their qubits to the field. In Chapter 6 we revisit a problem involving entanglement dynamics of two qubits subjected to Unruh acceleration and ask whether the existing results are perturbatively reliable. Finally, in Chapter 7 we discuss a slightly different but related topic that we call modest holography, a form of metric reconstruction in asymptotically flat spacetimes that relies on a bulk-to-boundary correspondence between the correlators of two different quantum field theories. We will see that the causal propagator plays different but essential roles in all of these subjects, possibly in ways that are more important than what it may seem at first sight. There is a sense in which one can argue that what makes relativistic quantum information relativistic is indeed the signaling component: it is about the causal structure of spacetime, and spacetime curvature provides the “details”.