Fundamental limitations on distillation of quantum channel resources
- URL: http://arxiv.org/abs/2010.11942v3
- Date: Sat, 17 Jul 2021 08:10:51 GMT
- Title: Fundamental limitations on distillation of quantum channel resources
- Authors: Bartosz Regula and Ryuji Takagi
- Abstract summary: We establish universal limitations on the processing of both quantum states and channels.
We focus on the class of distillation tasks, either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels.
We obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum channels underlie the dynamics of quantum systems, but in many
practical settings it is the channels themselves that require processing. We
establish universal limitations on the processing of both quantum states and
channels, expressed in the form of no-go theorems and quantitative bounds for
the manipulation of general quantum channel resources under the most general
transformation protocols. Focusing on the class of distillation tasks -- which
can be understood either as the purification of noisy channels into unitary
ones, or the extraction of state-based resources from channels -- we develop
fundamental restrictions on the error incurred in such transformations and
comprehensive lower bounds for the overhead of any distillation protocol. In
the asymptotic setting, our results yield broadly applicable bounds for rates
of distillation. We demonstrate our results through applications to
fault-tolerant quantum computation, where we obtain state-of-the-art lower
bounds for the overhead cost of magic state distillation, as well as to quantum
communication, where we recover a number of strong converse bounds for quantum
channel capacity.
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