dorsal/arxiv
View SchemaMulti-particle entanglement manipulation under positive partial transpose preserving operations
| Authors | Satoshi Ishizaka, Martin B. Plenio |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412193 |
| URL | https://arxiv.org/abs/quant-ph/0412193 |
| DOI | 10.1103/PhysRevA.71.052303 |
| Journal | Phys. Rev. A 71, 052303 (2005) |
Abstract
We consider the transformation of multi-partite states in the single copy setting under positive-partial-transpose-preserving operations (PPT-operations) and obtain both qualitative and quantitative results. Firstly, for some pure state transformations that are impossible under local operations and classical communication (LOCC), we demonstrate that they become possible with a surprisingly large success probability under PPT-operations. Furthermore, we clarify the convertibility of arbitrary multipartite pure states under PPT-operations, and show that a drastic simplification in the classification of pure state entanglement occurs when the set of operations is switched from LOCC to PPT-operations. Indeed, the infinitely many types of LOCC-incomparable entanglement are reduced to only one type under the action of PPT-operations. This is a clear manifestation of the increased power afforded by the use of PPT-bound entanglement. In addition, we further enlarge the set of operations to clarify the effect of another type of bound entanglement, multipartite unlockable bound entanglement, and show that a further simplification occurs. As compared to pure states a more complicated situation emerges in the mixed state settings. While single copy distillation becomes possible under PPT-operations for some mixed states it remains impossible for other mixed states.
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"abstract": "We consider the transformation of multi-partite states in the single copy\nsetting under positive-partial-transpose-preserving operations (PPT-operations)\nand obtain both qualitative and quantitative results. Firstly, for some pure\nstate transformations that are impossible under local operations and classical\ncommunication (LOCC), we demonstrate that they become possible with a\nsurprisingly large success probability under PPT-operations. Furthermore, we\nclarify the convertibility of arbitrary multipartite pure states under\nPPT-operations, and show that a drastic simplification in the classification of\npure state entanglement occurs when the set of operations is switched from LOCC\nto PPT-operations. Indeed, the infinitely many types of LOCC-incomparable\nentanglement are reduced to only one type under the action of PPT-operations.\nThis is a clear manifestation of the increased power afforded by the use of\nPPT-bound entanglement. In addition, we further enlarge the set of operations\nto clarify the effect of another type of bound entanglement, multipartite\nunlockable bound entanglement, and show that a further simplification occurs.\nAs compared to pure states a more complicated situation emerges in the mixed\nstate settings. While single copy distillation becomes possible under\nPPT-operations for some mixed states it remains impossible for other mixed\nstates.",
"arxiv_id": "quant-ph/0412193",
"authors": [
"Satoshi Ishizaka",
"Martin B. Plenio"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.052303",
"journal_ref": "Phys. Rev. A 71, 052303 (2005)",
"title": "Multi-particle entanglement manipulation under positive partial transpose preserving operations",
"url": "https://arxiv.org/abs/quant-ph/0412193"
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