Quantum hypothesis testing in many-body systems
- URL: http://arxiv.org/abs/2007.11711v3
- Date: Mon, 28 Jun 2021 09:33:03 GMT
- Title: Quantum hypothesis testing in many-body systems
- Authors: Jan de Boer, Victor Godet, Jani Kastikainen, Esko Keski-Vakkuri
- Abstract summary: In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing.
We consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 many-body 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 two-dimensional 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.
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