![]() ![]() They could also represent a first step towards a holographic description of measurement-induced phase transitions. Our results shed new light on the effects of measurement on the entanglement structure of holographic theories and give insight on how bulk information can be manipulated from the boundary theory. When A is the union of two disjoint subregions, the measurement triggers an entangled/disentangled phase transition between the remaining two unmeasured subregions, corresponding to a connected/disconnected phase transition in the bulk description. ![]() In semiclassical holography an arbitrary amount of bulk information can be teleported in this way, while in tensor network models the teleported information is upper-bounded by the amount of entanglement shared between A and A c due to finite- N effects. This suggests that LPMs performed on a boundary subregion A teleport part of the bulk information originally encoded in A into the complementary region A c. The post-measurement bulk dual to A c includes regions that were originally part of the entanglement wedge of A prior to measurement. Using a bulk calculation in AdS 3 and tensor network models of holography (in particular, the HaPPY code and random tensor networks), we show that the portions of the bulk geometry that are preserved after the measurement depend on the size of A and the state we project onto. We find that LPMs destroy portions of the bulk geometry, yielding post-measurement bulk spacetimes dual to the complementary unmeasured region A c that are cut off by end-of-the-world branes. In this paper, we describe how changes in the entanglement due to a local projective measurement (LPM) on a subregion A of the boundary theory modify the bulk dual spacetime. Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual theory. Throughout this analysis, we discuss the plethora of applications that arise in both astrophysics and fundamental theory before introducing a more realistic model adjusted for the inclusion of extended sources with limb-darkening effects. We present magnification curves using point-source models for numerous geometrical configurations involving different inclinations and spins. Utilising the expansions presented in, we consider gravitational lensing by a rotating, compact object (i.e an object described by the Kerr metric) in the weak deflection limit, thus assuming large astrophysical separations. The second part of this thesis involves gravitational lensing, the observed astrophysical phenomena involving the propagation of light through a specific background spacetime, governed by its null geodesic equations. We also explore alternate constructions of stabiliser codes for hyperbolic spaces in which the we associate the logical information with the boundary. We do so by considering both absolutely maximally entangled (AME) and non-AME codes noting that discrete symmetries of the polytope are always broken for AME codes in dimensions higher than two. We focus our attention on the study of codes associated with holographic geometries living in higher dimensions, constructing stabiliser codes that are analogues of the famous HaPPY code. Holographic properties have been vastly explored through the novel use of tensor networks, which can be interpreted as encoders for quantum error-correcting codes. The AdS/CFT correspondence is the most explicit realisation of the holographic principle, forming a unique framework in which one can use concepts and techniques arising in quantum information theory to study quantum gravity. According to the holographic principle, the fundamental degrees of freedom of a bulk spacetime are encoded on its boundary surface, which is of one dimension lower than the bulk. The first part of this thesis concerns itself with the suggestion that spacetime is not fundamental but rather an emergent concept. This thesis is dedicated to studying two particular topics that arose from explorations into the nature of spacetime and is correspondingly separated into two distinct parts, namely holographic quantum error-correcting codes and gravitational microlensing. The fabric of spacetime is the underlying structure embedding the entirety of the observable phenomena in our universe and though it has been studied in significant detail, many mysteries remain. ![]()
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