Randomizing quantum states in Shatten $p$-norms

Kabgyun Jeong

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arXiv · 1204.1813

Randomizing quantum states in Shatten $p$-norms

Kabgyun Jeong

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Abstract

In this paper, we formularize a method for randomizing quantum states with respect to the Schatten $p$-norm ($p\ge1$). Our theorem includes the Lemma 2.2 of Hayden and Winter [Commun. Math. Phys. {\bf 284}, 263--280 (2008)] for the norm case of $p>1$. We exploit the methods of a net construction on the unit sphere and McDiard's inequality in probability theory, and then we prove certain general cases (all $p$) of randomization tool for quantum states, which includes the operator norm and trace norm simultaneously in a single statement.

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BibTeX RIS

Kabgyun Jeong. 2012-04-09. Randomizing quantum states in Shatten $p$-norms. https://arxiv.org/abs/1204.1813

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