Device-independent lower bounds on the conditional von Neumann entropy
- URL: http://arxiv.org/abs/2106.13692v2
- Date: Fri, 28 Apr 2023 13:34:47 GMT
- Title: Device-independent lower bounds on the conditional von Neumann entropy
- Authors: Peter Brown, Hamza Fawzi and Omar Fawzi
- Abstract summary: We introduce a numerical method to compute lower bounds on rates of quantum protocols.
We find substantial improvements over all previous numerical techniques.
Our method is compatible with the entropy accumulation theorem.
- Score: 10.549307055348596
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The rates of several device-independent (DI) protocols, including quantum
key-distribution (QKD) and randomness expansion (RE), can be computed via an
optimization of the conditional von Neumann entropy over a particular class of
quantum states. In this work we introduce a numerical method to compute lower
bounds on such rates. We derive a sequence of optimization problems that
converge to the conditional von Neumann entropy of systems defined on general
separable Hilbert spaces. Using the Navascu\'es-Pironio-Ac\'in hierarchy we can
then relax these problems to semidefinite programs, giving a computationally
tractable method to compute lower bounds on the rates of DI protocols. Applying
our method to compute the rates of DI-RE and DI-QKD protocols we find
substantial improvements over all previous numerical techniques, demonstrating
significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD
we show a minimal detection efficiency threshold which is within the realm of
current capabilities. Moreover, we demonstrate that our method is capable of
converging rapidly by recovering all known tight analytical bounds up to
several decimal places. Finally, we note that our method is compatible with the
entropy accumulation theorem and can thus be used to compute rates of finite
round protocols and subsequently prove their security.
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