Quantum State Merging and Negative Information

By Michal Horodecki, Jonathan Oppenheim, Andreas J. Winter. 2005

330 citations recorded by the source corpus.

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.

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

View Paper: https://www.semanticscholar.org/paper/fcaf547926d29e0220c6b4ab86cda1eb2155886f

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Holographic duality from random tensor networks (2016, methodology): “) While the original proof of the multipartite entanglement of assistance formula used classically-inspired random coding information theory techniques, subsequent proofs proceeded by performing appropriate isotropic measurements of the C subsystems [40, 49].”
The Theory of Quantum Information (2018, background): “Horodecki, Oppenheim, and Winter [118] and Abeyesinghe, Devetak, Hayden, and Winter [1].”
A Generalization of Quantum Stein’s Lemma (2009, background): “Then Proof Let ρ = =1 p i | i i , with d = rank ( ρ ) , and Then from e.g. [52] (appendix C) we have and (cid:0) Hence from Eq.”
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].”
Multiboundary wormholes and holographic entanglement (2014, methodology): “(In fact, there is a single LOCC distillation procedure that will simultaneously extract both the B1 : B3 and the B2 : B3 entanglement at the specified rates in this case [54].”
An intuitive proof of the data processing inequality (2011, methodology): “Other approaches have used the operational meaning of the von Neumann entropy [9,10], Minkowski inequalities [11,12], or holographic gravity theory [13,14].”
The mother of all protocols: restructuring quantum information’s family tree (2006, methodology): “To start, it places the state merging protocol of Horodecki, Oppenheim and Winter [12, 13] squarely within the mother’s brood.”
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, methodology): “Quantum State Merging was introduced by Horodecki et al. in [30, 31].”
Integral geometry and holography (2015, background): “In quantum information theory, the conditional entropy acquires a direct operational meaning [39, 40]; a related operationalization of eq.”
A Survey on Quantum Channel Capacities (2018, methodology): “ssible applications of quantum relative entropy in quantum information processing were introduced by Vedral [524]. About the negativity of quantum information see the works of Horodecki et al. [237], [238]. About the use of entanglement in quantum information theory, see the work of Li et al. from 2”
The Operational Meaning of Min- and Max-Entropy (2008, background): “In fact, the -part of this statement is a direct consequence of decoupling result above [12], the arguments in [11] (cf.”