TY - JOUR

T1 - Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings

AU - Junge, Marius

AU - Laracuente, Nicholas

N1 - Funding Information:
N.L. was supported by IBM as a Postdoctoral Scholar at the University of Chicago and The Chicago Quantum Exchange. N.L. was previously supported by the Department of Physics at the University of Illinois at Urbana-Champaign. M.J. was partially supported by the NSF under Grant Nos. DMS 1800872 and Raise-TAQS 1839177.
Publisher Copyright:
© 2022 Author(s).

PY - 2022/12/1

Y1 - 2022/12/1

N2 - Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing the channel on both input states.

AB - Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing the channel on both input states.

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U2 - 10.1063/5.0066653

DO - 10.1063/5.0066653

M3 - Article

AN - SCOPUS:85144405264

SN - 0022-2488

VL - 63

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 12

M1 - 122204

ER -