The mother of all protocols: restructuring quantum information’s family tree

By Anura Abeyesinghe, Igor Devetak, Patrick M. Hayden, Andreas J. Winter. Proceedings of the Royal Society A, 2006

265 citations recorded by the source corpus.

We give a simple, direct proof of the ‘mother’ protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian–Wolf protocol, simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation and state transfer from the sender to the receiver. As a result, in addition to her other ‘children’, the mother protocol generates the state-merging primitive of Horodecki, Oppenheim and Winter, a fully quantum reverse Shannon theorem, and a new class of distributed compression protocols for correlated quantum sources which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called ‘father’ protocol whose children provide the quantum capacity and the entanglement-assisted capacity of a quantum channel, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.

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

View Paper: https://www.semanticscholar.org/paper/5fb6ff8b41fe61a83645daf532eb16812ec1b370

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Citations in the corpus

Local random quantum circuits are approximate polynomial-designs: numerical results (2012, methodology): “3 of [2]) E ( (U † 23 ⊗ U † 23)(F2:2 ⊗ I33)(U23 ⊗ U23) )”
Statistical mechanics of quantum error correcting codes (2020, background): “[49] A.”
Random Quantum Circuits are Approximate 2-designs (2008, methodology): “model the evolution of black holes [22]. In Ref. [22], they conjecture that short random local quantum circuits are approximately 2-designs, and thus can be used for decoupling quantum systems (as in [2]). This, in turn, is used to make claims about the rate at which black holes leak information. Wh”
The Church of the Symmetric Subspace (2013, background): “ter eect on the expectation. These techniques have been useful in quantum information theory for proving concentration bounds, for example in [7], where a moment generating function was used, and in [1], where bounding the second moment was sucient to produce powerful results. One reason that g(x) =”
Quantum channels and memory effects (2012, background): “An unification of these quantities under a common formalism based on resource inequalities has been presented in (Abeyesinghe and Hayden, 32 2003; Abeyesinghe et al., 2009; Devetak, Harrow, and Winter, 2004, 2008; Hsieh and Wilde, 2010 a,b).”
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, methodology): “It has since become an important tool in quantum information processing and was subsequently reformulated in [32], where it is called mother protocol .”
The Theory of Quantum Information (2018, background): “Horodecki, Oppenheim, and Winter [118] and Abeyesinghe, Devetak, Hayden, and Winter [1].”
Exponential Decay of Correlations Implies Area Law (2012, methodology): “…systems by performing a random measurement in one of them – an idea that has been used to derive the best known protocols for a variety of information theoretic tasks [43, 52, 53, 55, 56, 65, 66]) – as well as recent developments in the framework of single-shot quantum information theory [37, 60].”
A mathematical theory of resources (2014, unknown): “nd athermality [13]. More generally, one seeks to determine the asymptotic rates of conversion among processes (including states as special cases). The resource inequalities of quantum Shannon theory [22,1] is an example of such work. The fact that different sorts of resources can parallel-compose d”
Unbounded Violation of Tripartite Bell Inequalities (2007, background): “This theorem shows once more that random states exhibit unexpected extremal properties [ 1 ,14,35,36,50,80].”
Quantum entanglement (2007, unknown): “In (Abeyesinghe et al., 2006) a different version of state merging (called Fully Quantum Slepian Wolf protocol), where only quantum communication and sharing EPR pairsis allowed (and counted) was provided.”