Abstract
AbstractWe prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite dimensional GNS-symmetric quantum channel satisfies a strong data processing inequality with respect to its decoherence free part. Moreover, we establish the first general approximate tensorization property of the relative entropy. This extends the famous strong subadditivity of the quantum entropy (SSA) of two subsystems to the general setting of two subalgebras. All three results are independent of the size of the environment and hence satisfy the tensorization property. They are obtained via a common, conceptually simple method for proving entropic inequalities via spectral or $$L_2$$
L
2
-estimates. As an application, we combine our results on the modified log-Sobolev inequality and approximate tensorization to derive tight bounds for local generators.
Funder
DFG MCQST Start fellowship
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mathematics (miscellaneous),Analysis
Reference82 articles.
1. Aharonov, D., Arad, I., Landau, Z., Vazirani, U.: The detectability lemma and quantum gap amplification. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 417–426, 2009
2. Aharonov, D., Arad, I., Landau, Z., Vazirani, U.: Quantum Hamiltonian complexity and the detectability lemma. arXiv preprint arXiv:1011.3445, 2010
3. Ahlswede, R., Gács, P.: Spreading of sets in product spaces and hypercontraction of the Markov operator. Ann. Probab. 4, 925–939, 1976
4. Anshu, A., Arad, I., Vidick, T.: Simple proof of the detectability lemma and spectral gap amplification. Phys. Rev. B 93(20), 205142, 2016
5. Baillet, M., Denizeau, Y., Havet, J.-F.: Indice d’une espérance conditionnelle. Compositio Mathematica 66(2), 199–236, 1988
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