dorsal/arxiv
View SchemaOn Strong Superadditivity of the Entanglement of Formation
| Authors | Koenraad M. R. Audenaert, Samuel L. Braunstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0303045 |
| URL | https://arxiv.org/abs/quant-ph/0303045 |
| DOI | 10.1007/s00220-003-0987-1 |
| Journal | Communications in Mathematical Physics (246) No 3, 443-452, (2004) |
Abstract
We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation $E_F$ and the conjugate function $E^*$ of the entanglement function $E(\rho)=S(\trace_A\rho)$. We then consider the conjectured strong superadditivity of the entanglement of formation $E_F(\rho) \ge E_F(\rho_I)+E_F(\rho_{II})$, where $\rho_I$ and $\rho_{II}$ are the reductions of $\rho$ to the different Hilbert space copies, and prove that it is equivalent with subadditivity of $E^*$. As an application, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for all non-trace-preserving quantum channels, when purity is measured by Schatten $p$-norms for $p$ tending to 1.
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"abstract": "We employ a basic formalism from convex analysis to show a simple relation\nbetween the entanglement of formation $E_F$ and the conjugate function $E^*$ of\nthe entanglement function $E(\\rho)=S(\\trace_A\\rho)$. We then consider the\nconjectured strong superadditivity of the entanglement of formation $E_F(\\rho)\n\\ge E_F(\\rho_I)+E_F(\\rho_{II})$, where $\\rho_I$ and $\\rho_{II}$ are the\nreductions of $\\rho$ to the different Hilbert space copies, and prove that it\nis equivalent with subadditivity of $E^*$. As an application, we show that\nstrong superadditivity would follow from multiplicativity of the maximal\nchannel output purity for all non-trace-preserving quantum channels, when\npurity is measured by Schatten $p$-norms for $p$ tending to 1.",
"arxiv_id": "quant-ph/0303045",
"authors": [
"Koenraad M. R. Audenaert",
"Samuel L. Braunstein"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-003-0987-1",
"journal_ref": "Communications in Mathematical Physics (246) No 3, 443-452, (2004)",
"title": "On Strong Superadditivity of the Entanglement of Formation",
"url": "https://arxiv.org/abs/quant-ph/0303045"
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