Continuity of quantum conditional information

By Robert Alicki, M. Fannes. 2003

295 citations recorded by the source corpus.

We prove continuity of quantum conditional information S(ρ12|ρ2) with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This can, e.g., be used to prove the continuity of squashed entanglement.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/72fe77357b3e18d2f20aea780b15d0a7a3caaf3b

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints (2015, methodology): “Alicki and Fannes [1] proved an extension of the Fannes inequality for the conditional entropy S(A|B)ρ = S(ρAB)− S(ρB), defined for states ρ on a bipartite (tensor product) Hilbert space A ⊗ B.”
Faithful Squashed Entanglement (2010, background): “1 n [14] ? y [26] y y y [27] n LOCC monotonicitya y y y y y y y y [28] asymptotic continuity y [29] ? ? ? y y [30] y [9] n[9] convexity y ? ? ? y y y [31] n strong superadditivity y y y ? n [32, 33] n [34] ? ? subadditivity y ? ? y y y y y monogamy y [11] ? ? n [10] n [10] n [10] n [10] ?”
The mother of all protocols: restructuring quantum information’s family tree (2006, unknown): “followed by the Alicki-Fannes inequality [25].”
A Tight Uniform Continuity Bound for Equivocation (2019, background): “On the other hand, uniform bounds, which are not tight but are independent of the size of the conditioning system, were proven for the conditional Shannon and von Neumann entropies in [10], [8].”
Differential Privacy as a Mutual Information Constraint (2016, background): “The following lemma is inspired by ideas from [7] which in turn come from [2].”
Quantum Conditional Mutual Information and Approximate Markov Chains (2014, background): “The entropy difference on the right hand side can be bounded by the Alicki–Fannes inequality [1] in terms of the trace distance between the two states, yielding4 I (A : C |B)ρ ≤ 8 log2(dim A) − 4 log2(2 ) − 2(1 − 2 ) log2(1 − 2 ) for ≤ 1 2 .”