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Entanglement Theory Quantum Correlations Open Quantum Systems Decoherence Quantum Simulation

Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms

arXiv

Authors: Oded Regev, Thomas Vidick

Year

2012

Paper ID

8541

Status

Preprint

Abstract Read

~2 min

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Abstract

We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Invent. Math. 2002) and Haagerup and Musat (Invent. Math. 2008). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.

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We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Invent.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1206.4025 [2] arXiv https://arxiv.org/abs/1206.4025 [3] Publisher https://arxiv.org/abs/1206.4025

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