dorsal/arxiv
View SchemaA complete characterization of mixed state entanglement using probability density functions
| Authors | Shanthanu Bhardwaj, V. Ravishankar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703017 |
| URL | https://arxiv.org/abs/quant-ph/0703017 |
Abstract
We propose that the entanglement of mixed states is characterised properly in terms of a probability density function $\mathcal{P}(\mathcal{E})$. There is a need for such a measure since the prevalent measures (such as \textit{concurrence} and \textit{negativity}) are rough benchmarks, and not monotones of each other. Considering the specific case of two qubit mixed states, we provide an explicit construction of $\mathcal{P}(\mathcal{E})$ and show that it is characterised by a set of parameters, of which concurrence is but one particular combination. $\mathcal{P}(\mathcal{E})$ is manifestly invariant under $SU(2) \times SU(2)$ transformations. It can, in fact, reconstruct the state up to local operations - with the specification of at most four additional parameters. Finally the new measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.
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"abstract": "We propose that the entanglement of mixed states is characterised properly in\nterms of a probability density function $\\mathcal{P}(\\mathcal{E})$. There is a\nneed for such a measure since the prevalent measures (such as\n\\textit{concurrence} and \\textit{negativity}) are rough benchmarks, and not\nmonotones of each other. Considering the specific case of two qubit mixed\nstates, we provide an explicit construction of $\\mathcal{P}(\\mathcal{E})$ and\nshow that it is characterised by a set of parameters, of which concurrence is\nbut one particular combination. $\\mathcal{P}(\\mathcal{E})$ is manifestly\ninvariant under $SU(2) \\times SU(2)$ transformations. It can, in fact,\nreconstruct the state up to local operations\n - with the specification of at most four additional parameters. Finally the\nnew measure resolves the controversy regarding the role of entanglement in\nquantum computation in NMR systems.",
"arxiv_id": "quant-ph/0703017",
"authors": [
"Shanthanu Bhardwaj",
"V. Ravishankar"
],
"categories": [
"quant-ph",
"cond-mat.other",
"hep-th"
],
"title": "A complete characterization of mixed state entanglement using probability density functions",
"url": "https://arxiv.org/abs/quant-ph/0703017"
},
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