dorsal/arxiv
View SchemaOn the communication cost of entanglement transformations
| Authors | Patrick Hayden, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204092 |
| URL | https://arxiv.org/abs/quant-ph/0204092 |
| DOI | 10.1103/PhysRevA.67.012326 |
| Journal | Phys. Rev. A 67, 012326 (2003) |
Abstract
We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR pairs, and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462, 1999], requires a number of bits to be exchanged which is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of ``embezzling entanglement'' [W. van Dam and P. Hayden, quant-ph/0201041].
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"abstract": "We study the amount of communication needed for two parties to transform some\ngiven joint pure state into another one, either exactly or with some fidelity.\nSpecifically, we present a method to lower bound this communication cost even\nwhen the amount of entanglement does not increase. Moreover, the bound applies\neven if the initial state is supplemented with unlimited entanglement in the\nform of EPR pairs, and the communication is allowed to be quantum mechanical.\n We then apply the method to the determination of the communication cost of\nasymptotic entanglement concentration and dilution. While concentration is\nknown to require no communication whatsoever, the best known protocol for\ndilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462,\n1999], requires a number of bits to be exchanged which is of the order of the\nsquare root of the number of EPR pairs. Here we prove a matching lower bound of\nthe same asymptotic order, demonstrating the optimality of the Lo-Popescu\nprotocol up to a constant factor and establishing the existence of a\nfundamental asymmetry between the concentration and dilution tasks.\n We also discuss states for which the minimal communication cost is\nproportional to their entanglement, such as the states recently introduced in\nthe context of ``embezzling entanglement\u0027\u0027 [W. van Dam and P. Hayden,\nquant-ph/0201041].",
"arxiv_id": "quant-ph/0204092",
"authors": [
"Patrick Hayden",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.67.012326",
"journal_ref": "Phys. Rev. A 67, 012326 (2003)",
"title": "On the communication cost of entanglement transformations",
"url": "https://arxiv.org/abs/quant-ph/0204092"
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