288 research outputs found
Perturbative calculation of quasi-normal modes
I discuss a systematic method of analytically calculating the asymptotic form
of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild
black hole, I expand around the zeroth-order approximation to the wave equation
proposed by Motl and Neitzke. In the case of a five-dimensional AdS black hole,
I discuss a perturbative solution of the Heun equation. The analytical results
are in agreement with the results from numerical analysis.Comment: 7 pages, presented at PASCOS 2004 / Nath Fes
Practically secure quantum position verification
We discuss quantum position verification (QPV) protocols in which the
verifiers create and send single-qubit states to the prover. QPV protocols
using single-qubit states are known to be insecure against adversaries that
share a small number of entangled qubits. We introduce QPV protocols that are
practically secure: they only require single-qubit states from each of the
verifiers, yet their security is broken if the adversaries share an
impractically large number of shared entangled qubits. These protocols are a
modification of known QPV protocols in which we include a classical random
oracle without altering the amount of quantum resources needed by the
verifiers. We present a cheating strategy that requires a number of entangled
qubits shared among the adversaries that grows exponentially with the size of
the classical input of the random oracle.Comment: v2: corrected errors, more detailed discussio
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