Strong converse for identification via quantum channels

By R. Ahlswede, Andreas J. Winter. IEEE Transactions on Information Theory, 2000

531 citations recorded by the source corpus.

We present a simple proof of the strong converse for identification via discrete memoryless quantum channels, based on a novel covering lemma. The new method is a generalization to quantum communication channels of Ahlswede's (1979, 1992) approach to classical channels. It involves a development of explicit large deviation estimates to the case of random variables taking values in self-adjoint operators on a Hilbert space. This theory is presented separately in an appendix, and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/3872d48be875096dbf38612d762962630b687d40

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Citations in the corpus

A Method of Moments for Mixture Models and Hidden Markov Models (2012, background): “Proof This is a direct corollary of Theorem 19 from Ahlswede and Winter (2002).”
Noncommutative Bennett and Rosenthal inequalities (2011, methodology): “Indeed, in [1] the Bernstein inequality applies to independent random variables in a von Neumann algebra and gives information about the random spectrum.”
Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges (2009, methodology): “The proof of Theorem 1.2 follows a methodology ﬁrst proposed by Ahlswede and Winter [2].”
An Overview of Low-Rank Matrix Recovery From Incomplete Observations (2016, methodology): “Under this model, one can analyze the adjoint operator A ∗ ( ) by treating its output as a sum of independent random matrices, which enables the use of the powerful concentration inequalities recently developed in [2] that bound the deviation of this sum from its expected value.”
A ug 2 01 4 Local Privacy , Data Processing Inequalities , and Minimax Rates (2018, background): “This bound does not depend on the norm for X so long as p ∈ [1, 2], which is consistent with the classical mean estimation problem.”
User-Friendly Tail Bounds for Sums of Random Matrices (2010, methodology): “We begin our main development with a striking idea drawn from the influential paper [AW02] of Ahlswede and Winter.”
Interlacing families II: Mixed characteristic polynomials and the Kadison{Singer problem (2013, result): “If ε > 0 and v 1 , . . . , v m are independent random vectors in C d with ﬁnite support such that The above theorem may be compared to the concentration inequalities of Rudelson [46] and Ahlswede and Winter [1], which imply in our setting that · log n with high probability.”
A Simpler Approach to Matrix Completion (2009, methodology): “2 is a corollary of an Che rnoff bound for finite dimensional operators developed by Ahlswede and Winter [1].”
Entanglement of assistance and multipartite state distillation (2005, background): “⊓⊔ Lemma 12 (Density sampling [2]) Consider the ensemble ( q j , ρ j ) of states on a d -dimensional Hilbert space, with average density operator ρ and Holevo information χ .”