Security of quantum key distribution

By Renato Renner. Ausgezeichnete Informatikdissertationen, 2005

1,473 citations recorded by the source corpus.

Quantum Information Theory is an area of physics which studies both fundamental and applied issues in quantum mechanics from an information-theoretical viewpoint. The underlying techniques are, however, often restricted to the analysis of systems which satisfy a certain independence condition. For example, it is assumed that an experiment can be repeated independently many times or that a large physical system consists of many virtually independent parts. Unfortunately, such assumptions are not always justified. This is particularly the case for practical applications — e.g. in quantum cryptography — where parts of a system might have an arbitrary and unknown behavior. We propose an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold. It is based on an extension of various information-theoretical notions. For example, we introduce new uncertainty measures, called smooth min- and max-entropy, which are generalizations of ...

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/022f4ca76b07470a6ef1824fa546e5b093a9fbf2

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Citations in the corpus

A Generalization of Quantum Stein’s Lemma (2009, methodology): “The main ingredient of the proof is a variant of Renner’s exponential version of the quantum de Finetti theorem [20, 21] (see Appendix B), given in Lemma III.5.”
Min- and Max-Relative Entropies and a New Entanglement Monotone (2008, background): “(13) The min- and max-entropies of a bipartite state, ρAB, relative to a state σB, are similarly obtained by setting σ = IA ⊗ σB : Hmin(ρAB|σB) := − logmin{λ : ρAB ≤ λ · IA ⊗ ρB} = −Dmax(ρAB ||IA ⊗ σB) (14) and Hmax(ρAB|σB) := log Tr ( πAB(IA ⊗ σB) ) , = −Dmin(ρAB||IA ⊗ σB) (15) In the above, πAB…”
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, methodology): “[12, Lemma 5.1.3] Let S be a Hermitian operator on H and ξ ∈ P ( H ).”
Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations (2015, background): “More recently, a new paradigm for evaluating the security of QKD protocols has been put forward, notably by Renner [32], following the universal composability framework of Canetti [33].”
A Survey on Quantum Channel Capacities (2018, background): “This characteristics allow quantum based solutions to support absolute security, to which there have been abundant examples of quantum based solutions [176], [300], [302], [569], [553] where a popular example of mature applications is quantum key distribution (QKD) [53], [68].”
QBism, the Perimeter of Quantum Bayesianism (2010, background): “In fact, the quantum de Finetti theorem has long left its foundational roots behind and found far more widespread recognition with its applications to quantum cryptography [28].”
Quantum Cryptography (2006, positive): “We thus need a corresponding notion of min-entropy of a random variable conditioned on a quantum system: H∞(ρXE |E) for a hybrid state ρXE = ∑x PX(x)|x〉〈x| ⊗ ρ E ∈ D(HX ⊗ HE) with classical X; such a notion was introduced by Renner [49].”
Symmetry of large physical systems implies independence of subsystems (2007, background): “Our global 4 representation theorem can now be formulated as follows (see Appendix A for a more technical statement and Appendix B for a proof; see also [Ren05] for a preliminary version as well as [KM07] for a nice generalisation of the result FIG.”
The resource theory of informational nonequilibrium in thermodynamics (2013, methodology): “Finally, in various places (in particular in our discussion of measures of nonuniformity) we make use of work concerning the zoo of generalized entropies (Datta, 2009; van Erven and Harremoës, 2010; Gorban et al., 2010; Renner, 2008; Renner and Wolf, 2004).”
A device-independent quantum key distribution system for distant users (2021, methodology): “Both the QBERs (Q0, Q1) and the CHSH value S are used to determine the amount of information about the sifted key that could have been obtained by an eavesdropper [35].”
From Classical to Quantum Shannon Theory (2011, methodology): “(2015a) used the techniques of Fawzi and Renner (2015) to establish a non-trivial lower bound on a relative entropy difference. Datta and Wilde (2015) proved that ∆̃α(ρ, σ,N ) ≥ 0 for all α ∈ (1/2, 1) ∪ (1,∞) in addition to other related statements.”
A Fully Quantum Asymptotic Equipartition Property (2008, methodology): “We note that our proof technique is different from the one used in [9], where the result also explicitly depends on the dimension of the Hilbert space .”
The Church of the Symmetric Subspace (2013, background): “See [32] for more discussion of this point, [31] for an application to quantum key distribution or [16] for an application to mean-ﬁeld Hamiltonians.”