Jan de Boer, Victor Godet, Jani Kastikainen, Esko KeskiVakkuri
SciPost Phys. Core 4, 019 (2021) ·
published 23 June 2021

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One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning.
In this paper we consider the application of quantum hypothesis testing to quantum manybody systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and twodimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.
SciPost Phys. 8, 089 (2020) ·
published 17 June 2020

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We study gravitational perturbations around the near horizon geometry of the
(near) extreme Kerr black hole. By considering a consistent truncation for the
metric fluctuations, we obtain a solution to the linearized Einstein equations.
The dynamics is governed by two master fields which, in the context of the
nAdS$_2$/nCFT$_1$ correspondence, are both irrelevant operators of conformal
dimension $\Delta=2$. These fields control the departure from extremality by
breaking the conformal symmetry of the near horizon region. One of the master
fields is tied to large diffeomorphisms of the near horizon, with its equations
of motion compatible with a Schwarzian effective action. The other field is
essential for a consistent description of the geometry away from the horizon.