Partial quantum information

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

430 citations recorded by the source corpus.

Information—be it classical or quantum—is measured by the amount of communication needed to convey it. In the classical case, if the receiver has some prior information about the messages being conveyed, less communication is needed. Here we explore the concept of prior quantum information: given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the partial information one system needs, conditioned on its prior information. We find that it is given by the conditional entropy—a quantity that was known previously, but lacked an operational meaning. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, then sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a protocol that we term ‘quantum state merging’ which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, noiseless coding with side information, multiple access channels and assisted entanglement distillation.

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

View Paper: https://www.semanticscholar.org/paper/8a716a4c1afeaa7ec49f23c90f2dc0d7311fb08b

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

The mother of all protocols: restructuring quantum information’s family tree (2006, methodology): “For this problem, Horodecki, Oppenheim and Winter demonstrated that the resulting region of achievable rates has the same form as the classical Slepian-Wolf problem [12, 16].”
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.”
The classical-quantum boundary for correlations: Discord and related measures (2011, background): “The discords for a measurement on A are D(B|A) = 0.05, Dth(B|A) = 0.20, D(B|{ΠEiga }) = 0.21, (49) and the discords for a measurement on B are zero.”
Quantum coherence and geometric quantum discord (2017, background): “They discussed the protocol of quantum state merging under IO, which they called incoherent quantum state merging, and is indeed an analog of the standard state merging with general quantum operations (Horodecki et al., 2005b).”
A Survey on Quantum Channel Capacities (2018, methodology): “008 [428]. For the properties of Holevo information and on the capacity of quantum channels see the works of Holevo [231], [233], Schumacher and Westmoreland [464, 465, 466, 467, 468, 469], Horodecki [237], Datta [127], Arimoto [18]. On the geometrical interpretation of the maps of a quantum channel”
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].”
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, methodology): “Quantum State Merging, Quantum State Splitting, and other related quantum information processing primitives are discussed in detail in [15, 30–32 , 41 Deﬁnition III. where | φ L (cid:105)(cid:104) φ L | A 1 B 1 is a maximally entangled state of Schmidt-rank L and ρ B (cid:48) BR = ( I A → B…”