This thesis explores instances of the intersection of quantum mechanics and gravity using
tools from quantum information theory to apply it to gravity. We investigate the consistency
of Hawking’s black hole evaporation process with fundamental physical principles
such as unitarity, no-signaling, entanglement monogamy, and the equivalence principle.
The analysis suggests that standard quantum theory and general relativity can account
for the entire state consisting of matter and radiation, which remains pure at any stage of
the evaporation process. Furthermore, the final state after the full black hole evaporation
is pure and in one-to-one correspondence with the initial state forming the black hole,
indicating no information loss. We introduce controlled squeezing operators and show
tha...[

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This thesis explores instances of the intersection of quantum mechanics and gravity using
tools from quantum information theory to apply it to gravity. We investigate the consistency
of Hawking’s black hole evaporation process with fundamental physical principles
such as unitarity, no-signaling, entanglement monogamy, and the equivalence principle.
The analysis suggests that standard quantum theory and general relativity can account
for the entire state consisting of matter and radiation, which remains pure at any stage of
the evaporation process. Furthermore, the final state after the full black hole evaporation
is pure and in one-to-one correspondence with the initial state forming the black hole,
indicating no information loss. We introduce controlled squeezing operators and show
that after every squeezing the probability that the black hole evaporates increases. We
show as well that the evaporation process is a combination of controlled squeezing and
scattering S-matrices.

The singularity inside the black hole, however, can prevent the unitary scattering from
happening. To address the singularity issue, the second chapter derives the gravitational
field and the spacetime metric generated by sources in quantum superposition of different
locations. We there adopt two independent constructions, the first of which promotes the
potential to an operator and lets it act on the matter state, then covariant uplifting its
expectation value to derive the radial and temporal components of the metric. The second
approach writes down a joint superposition state for the matter and the corresponding spacetime metric, assuming that in each branch of the matter’s superposition the space-time
metric’s state follows GR and is fully determined by the Einstein equations. The The
resulting quantum corrected effective metric is consistent with that obtain with the first
method, but augments it in that it derives the angular components as well. In both cases
we work out the example of the matter is in a Gaussian state, with a certain width that
we call R. The physical system that the metric represents will differ depending on the
width of the Gaussian relative to its would-be Schwarzschild horizon. The solutions will
be categorized in three families according to whether the width is larger than r

_{s}, equal, or
smaller. This study provides a detailed exploration of the geometric and thermodynamic
properties of the spacetime structure for the three families of models, including nonsingular
black holes, one-way wormholes with a critical null throat, and traversable wormholes.

Despite suggesting a way to smear out the singularity, there are other difficulties that
might prevent the process that we described to happen. For instance, there are suggestions
in the literature that quantum states decohere near a black hole. This decoherence
or loss of quantumness can cause loss of information. For this reason,our third chapter investigates
the degradation in the performance of quantum communication protocols that
take place near a black hole due to quantum information being lost beyond the event
horizon. However, the study shows that when the quantum nature of a black hole and
its spacetime are taken into account, their quantum properties can be used as resources
to limit the amount of quantum information loss, improving the performance of quantum
communication protocols. This project extends the scope of recent results in quantum
foundations on the coherent control of quantum channels, indicating that quantum features
of spacetime could serve as resources for quantum information processing.

Finally, In order to probe the inside of the black hole, one looks for the quantum corrections
of the stress energy tensor behind the event horizon. In order to compute those
quantum corrections one can make use of its equivalence with the one-loop corrected effective
action, or in simpler cases the effective potential. However, this effective potential
is known to be gauge dependent. The fourth chapter highlights the necessity of resolving
the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We propose a practical shortcut to gauge-independent inflationary
observables by using effective potential obtained from a polar-like background
current choice. This study demonstrates this shortcut for several explicit examples and
presents a gauge-independent prediction of inflationary observables in the Abelian Higgs
model. Furthermore, the authors show that for any theory to all orders, the use of
a gauge-invariant current term gives a gauge-independent effective potential and thus
gauge-invariant inflationary observables. Together, these projects contribute to a better
understanding of the interaction between quantum mechanics and gravity and provide
insights into the quantum nature of black holes, spacetime, and inflationary observables.
The thesis often uses tools from quantum information theory to explore the intersection of
quantum mechanics and gravity, taking a conservative approach to combining quantum
mechanics and gravity, exploring the possibility of further quantum corrections or more
accurately adding more quantumness to classical and semi-classical scenarios.

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