dorsal/arxiv
View SchemaQuantum information can be negative
| Authors | Michal Horodecki, Jonathan Oppenheim, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505062 |
| URL | https://arxiv.org/abs/quant-ph/0505062 |
| DOI | 10.1038/nature03909 |
| Journal | Nature 436:673-676 (2005) as "Partial quantum information" |
Abstract
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 it's prior information. It turns out to be given by an extremely simple formula, the conditional entropy. 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, the sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a primitive "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, multiple access channels and multipartite assisted entanglement distillation (localizable entanglement). Negative channel capacities also receive a natural interpretation.
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"abstract": "Given an unknown quantum state distributed over two systems, we determine how\nmuch quantum communication is needed to transfer the full state to one system.\nThis communication measures the \"partial information\" one system needs\nconditioned on it\u0027s prior information. It turns out to be given by an extremely\nsimple formula, the conditional entropy. In the classical case, partial\ninformation must always be positive, but we find that in the quantum world this\nphysical quantity can be negative. If the partial information is positive, its\nsender needs to communicate this number of quantum bits to the receiver; if it\nis negative, the sender and receiver instead gain the corresponding potential\nfor future quantum communication. We introduce a primitive \"quantum state\nmerging\" which optimally transfers partial information. We show how it enables\na systematic understanding of quantum network theory, and discuss several\nimportant applications including distributed compression, multiple access\nchannels and multipartite assisted entanglement distillation (localizable\nentanglement). Negative channel capacities also receive a natural\ninterpretation.",
"arxiv_id": "quant-ph/0505062",
"authors": [
"Michal Horodecki",
"Jonathan Oppenheim",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1038/nature03909",
"journal_ref": "Nature 436:673-676 (2005) as \"Partial quantum information\"",
"title": "Quantum information can be negative",
"url": "https://arxiv.org/abs/quant-ph/0505062"
},
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