dorsal/arxiv
View SchemaQuantum network communication -- the butterfly and beyond
| Authors | Debbie Leung, Jonathan Oppenheim, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608223 |
| URL | https://arxiv.org/abs/quant-ph/0608223 |
| DOI | 10.1109/TIT.2010.2048442 |
| Journal | IEEE Trans. Inf. Theory, 56 (2010) 3478-3490 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We study the k-pair communication problem for quantum information in networks of quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs. Four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. (i) We obtain outer and inner bounds of the achievable rate regions in the most general directed networks. (ii) For two particular networks (including the butterfly network) routing is proved optimal, and the free assisting classical communication can at best be used to modify the directions of quantum channels in the network. Consequently, the achievable rate regions are given by counting edge avoiding paths, and precise achievable rate regions in all four assisting scenarios can be obtained. (iii) Optimality of routing can also be proved in classes of networks. The first class consists of directed unassisted networks in which (1) the receivers are information sinks, (2) the maximum distance from senders to receivers is small, and (3) a certain type of 4-cycles are absent, but without further constraints (such as on the number of communicating and intermediate parties). The second class consists of arbitrary backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair communication problem, observations are made on quantum multicasting and a static version of network communication related to the entanglement of assistance.
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"abstract": "We study the k-pair communication problem for quantum information in networks\nof quantum channels. We consider the asymptotic rates of high fidelity quantum\ncommunication between specific sender-receiver pairs. Four scenarios of\nclassical communication assistance (none, forward, backward, and two-way) are\nconsidered. (i) We obtain outer and inner bounds of the achievable rate regions\nin the most general directed networks. (ii) For two particular networks\n(including the butterfly network) routing is proved optimal, and the free\nassisting classical communication can at best be used to modify the directions\nof quantum channels in the network. Consequently, the achievable rate regions\nare given by counting edge avoiding paths, and precise achievable rate regions\nin all four assisting scenarios can be obtained. (iii) Optimality of routing\ncan also be proved in classes of networks. The first class consists of directed\nunassisted networks in which (1) the receivers are information sinks, (2) the\nmaximum distance from senders to receivers is small, and (3) a certain type of\n4-cycles are absent, but without further constraints (such as on the number of\ncommunicating and intermediate parties). The second class consists of arbitrary\nbackward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair\ncommunication problem, observations are made on quantum multicasting and a\nstatic version of network communication related to the entanglement of\nassistance.",
"arxiv_id": "quant-ph/0608223",
"authors": [
"Debbie Leung",
"Jonathan Oppenheim",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2010.2048442",
"journal_ref": "IEEE Trans. Inf. Theory, 56 (2010) 3478-3490",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Quantum network communication -- the butterfly and beyond",
"url": "https://arxiv.org/abs/quant-ph/0608223"
},
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