dorsal/arxiv
View SchemaConcentrating entanglement by local actions---beyond mean values
| Authors | Hoi-Kwong Lo, Sandu Popescu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9707038 |
| URL | https://arxiv.org/abs/quant-ph/9707038 |
Abstract
Suppose two distant observers Alice and Bob share a pure bipartite quantum state. By applying local operations and communicating with each other using a classical channel, Alice and Bob can manipulate it into some other states. Previous investigations of entanglement manipulations have been largely limited to a small number of strategies and their average outcomes. Here we consider a general entanglement manipulation strategy and go beyond the average property. For a pure entangled state shared between two separated persons Alice and Bob, we show that the mathematical interchange symmetry of the Schmidt decomposition can be promoted into a physical symmetry between the actions of Alice and Bob. Consequently, the most general (multi-step two-way-communications) strategy of entanglement manipulation of a pure state is, in fact, equivalent to a strategy involving only a single (generalized) measurement by Alice followed by one-way communications of its result to Bob. We also prove that strategies with one-way communications are generally more powerful than those without communications. In summary, one-way communications is necessary and sufficient for the entanglement manipulations of a pure bipartite state. The supremum probability of obtaining a maximally entangled state (of any dimension) from an arbitrary state is determined and a strategy for achieving this probability is constructed explicitly. One important question is whether collective manipulations in quantum mechanics can greatly enhance the probability of large deviations from the average behavior. We answer this question in the negative for a specific problem.
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"abstract": "Suppose two distant observers Alice and Bob share a pure bipartite quantum\nstate. By applying local operations and communicating with each other using a\nclassical channel, Alice and Bob can manipulate it into some other states.\nPrevious investigations of entanglement manipulations have been largely limited\nto a small number of strategies and their average outcomes. Here we consider a\ngeneral entanglement manipulation strategy and go beyond the average property.\nFor a pure entangled state shared between two separated persons Alice and Bob,\nwe show that the mathematical interchange symmetry of the Schmidt decomposition\ncan be promoted into a physical symmetry between the actions of Alice and Bob.\nConsequently, the most general (multi-step two-way-communications) strategy of\nentanglement manipulation of a pure state is, in fact, equivalent to a strategy\ninvolving only a single (generalized) measurement by Alice followed by one-way\ncommunications of its result to Bob. We also prove that strategies with one-way\ncommunications are generally more powerful than those without communications.\nIn summary, one-way communications is necessary and sufficient for the\nentanglement manipulations of a pure bipartite state. The supremum probability\nof obtaining a maximally entangled state (of any dimension) from an arbitrary\nstate is determined and a strategy for achieving this probability is\nconstructed explicitly. One important question is whether collective\nmanipulations in quantum mechanics can greatly enhance the probability of large\ndeviations from the average behavior. We answer this question in the negative\nfor a specific problem.",
"arxiv_id": "quant-ph/9707038",
"authors": [
"Hoi-Kwong Lo",
"Sandu Popescu"
],
"categories": [
"quant-ph"
],
"title": "Concentrating entanglement by local actions---beyond mean values",
"url": "https://arxiv.org/abs/quant-ph/9707038"
},
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