dorsal/arxiv
View SchemaLocal versus non-local information in quantum information theory: formalism and phenomena
| Authors | Michal Horodecki, Pawel Horodecki, Ryszard Horodecki, Jonathan Oppenheim, Aditi Sen De, Ujjwal Sen, Barbara Synak |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410090 |
| URL | https://arxiv.org/abs/quant-ph/0410090 |
| DOI | 10.1103/PhysRevA.71.062307 |
| Journal | Phys. Rev. A 71, 062307 (2005) |
Abstract
In spite of many results in quantum information theory, the complex nature of compound systems is far from being clear. In general the information is a mixture of local, and non-local ("quantum") information. To make this point more clear, we develop and investigate the quantum information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm, we show that the upper bound for the deficit is given by the relative entropy distance to so-called psuedo-classically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal i.e. has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other non-local phenomena. For example,we prove the existence of a form of non-locality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal (and in fact can be thought of as quasi-nonlocalisable). We also show that there do not exist states, for which the deficit is strictly equal to the whole informational content (bound local information). We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.
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"abstract": "In spite of many results in quantum information theory, the complex nature of\ncompound systems is far from being clear. In general the information is a\nmixture of local, and non-local (\"quantum\") information. To make this point\nmore clear, we develop and investigate the quantum information processing\nparadigm in which parties sharing a multipartite state distill local\ninformation. The amount of information which is lost because the parties must\nuse a classical communication channel is the deficit. This scheme can be viewed\nas complementary to the notion of distilling entanglement. After reviewing the\nparadigm, we show that the upper bound for the deficit is given by the relative\nentropy distance to so-called psuedo-classically correlated states; the lower\nbound is the relative entropy of entanglement. This implies, in particular,\nthat any entangled state is informationally nonlocal i.e. has nonzero deficit.\nWe also apply the paradigm to defining the thermodynamical cost of erasing\nentanglement. We show the cost is bounded from below by relative entropy of\nentanglement. We demonstrate the existence of several other non-local\nphenomena. For example,we prove the existence of a form of non-locality without\nentanglement and with distinguishability. We analyze the deficit for several\nclasses of multipartite pure states and obtain that in contrast to the GHZ\nstate, the Aharonov state is extremely nonlocal (and in fact can be thought of\nas quasi-nonlocalisable). We also show that there do not exist states, for\nwhich the deficit is strictly equal to the whole informational content (bound\nlocal information). We then discuss complementary features of information in\ndistributed quantum systems. Finally we discuss the physical and theoretical\nmeaning of the results and pose many open questions.",
"arxiv_id": "quant-ph/0410090",
"authors": [
"Michal Horodecki",
"Pawel Horodecki",
"Ryszard Horodecki",
"Jonathan Oppenheim",
"Aditi Sen De",
"Ujjwal Sen",
"Barbara Synak"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.062307",
"journal_ref": "Phys. Rev. A 71, 062307 (2005)",
"title": "Local versus non-local information in quantum information theory: formalism and phenomena",
"url": "https://arxiv.org/abs/quant-ph/0410090"
},
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