dorsal/arxiv
View SchemaUnextendible product bases and locally unconvertible bound entangled states
| Authors | Sergey Bravyi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310172 |
| URL | https://arxiv.org/abs/quant-ph/0310172 |
| Journal | Quantum Information Processing, Vol. 3(6) pp. 309-329 (2004) |
Abstract
Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs $S$ and $T$ the associated bound entangled states $\rho_S$ and $\rho_T$ can not be converted to each other by LOCC, unless $S$ and $T$ coincide up to local unitaries. More specifically, there exists a finite precision $\epsilon>0$ such that for any LOCC protocol mapping $\rho_S$ into a probabilistic ensemble $(p_j,\rho_j)$, the fidelity between $\rho_T$ and any possible final state $\rho_j$ is smaller than $1-\epsilon$.
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"abstract": "Mutual convertibility of bound entangled states under local quantum\noperations and classical communication (LOCC) is studied. We focus on states\nassociated with unextendible product bases (UPB) in a system of three qubits. A\ncomplete classification of such UPBs is suggested. We prove that for any pair\nof UPBs $S$ and $T$ the associated bound entangled states $\\rho_S$ and $\\rho_T$\ncan not be converted to each other by LOCC, unless $S$ and $T$ coincide up to\nlocal unitaries. More specifically, there exists a finite precision\n$\\epsilon\u003e0$ such that for any LOCC protocol mapping $\\rho_S$ into a\nprobabilistic ensemble $(p_j,\\rho_j)$, the fidelity between $\\rho_T$ and any\npossible final state $\\rho_j$ is smaller than $1-\\epsilon$.",
"arxiv_id": "quant-ph/0310172",
"authors": [
"Sergey Bravyi"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information Processing, Vol. 3(6) pp. 309-329 (2004)",
"title": "Unextendible product bases and locally unconvertible bound entangled states",
"url": "https://arxiv.org/abs/quant-ph/0310172"
},
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