Tight concentration inequalities for quantum adversarial setups exploiting permutation symmetry
arxiv(2024)
摘要
We developed new concentration inequalities for a quantum state on an
N-qudit system or measurement outcomes on it that apply to an adversarial
setup, where an adversary prepares the quantum state. Our one-sided
concentration inequalities for a quantum state require the N-qudit system to
be permutation invariant and are thus de-Finetti type, but they are tighter
than the one previously obtained. We show that the bound can further be
tightened if each qudit system has an additional symmetry. Furthermore, our
concentration inequality for the outcomes of independent and identical
measurements on an N-qudit quantum system has no assumption on the
adversarial quantum state and is much tighter than the conventional one
obtained through Azuma's inequality. We numerically demonstrate the tightness
of our bounds in simple quantum information processing tasks.
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