dorsal/arxiv
View SchemaFerreting out the Fluffy Bunnies: Entanglement constrained by Generalized superselection rules
| Authors | Howard M. Wiseman, Stephen D. Bartlett, John A. Vaccaro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0309046 |
| URL | https://arxiv.org/abs/quant-ph/0309046 |
| DOI | 10.1142/9789812703002_0047 |
Abstract
Entanglement is a resource central to quantum information (QI). In particular, entanglement shared between two distant parties allows them to do certain tasks that would otherwise be impossible. In this context, we study the effect on the available entanglement of physical restrictions on the local operations that can be performed by the two parties. We enforce these physical restrictions by generalized superselection rules (SSRs), which we define to be associated with a given group of physical transformations. Specifically the generalized SSR is that the local operations must be covariant with respect to that group. Then we operationally define the entanglement constrained by a SSR, and show that it may be far below that expected on the basis of a naive (or ``fluffy bunny'') calculation. We consider two examples. The first is a particle number SSR. Using this we show that for a two-mode BEC (with Alice owning mode $A$ and Bob mode $B$), the useful entanglement shared by Alice and Bob is identically zero. The second, a SSR associated with the symmetric group, is applicable to ensemble QI processing such as in liquid-NMR. We prove that even for an ensemble comprising many pairs of qubits, with each pair described by a pure Bell state, the entanglement per pair constrained by this SSR goes to zero for a large ensemble.
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"abstract": "Entanglement is a resource central to quantum information (QI). In\nparticular, entanglement shared between two distant parties allows them to do\ncertain tasks that would otherwise be impossible. In this context, we study the\neffect on the available entanglement of physical restrictions on the local\noperations that can be performed by the two parties. We enforce these physical\nrestrictions by generalized superselection rules (SSRs), which we define to be\nassociated with a given group of physical transformations. Specifically the\ngeneralized SSR is that the local operations must be covariant with respect to\nthat group. Then we operationally define the entanglement constrained by a SSR,\nand show that it may be far below that expected on the basis of a naive (or\n``fluffy bunny\u0027\u0027) calculation. We consider two examples. The first is a\nparticle number SSR. Using this we show that for a two-mode BEC (with Alice\nowning mode $A$ and Bob mode $B$), the useful entanglement shared by Alice and\nBob is identically zero. The second, a SSR associated with the symmetric group,\nis applicable to ensemble QI processing such as in liquid-NMR. We prove that\neven for an ensemble comprising many pairs of qubits, with each pair described\nby a pure Bell state, the entanglement per pair constrained by this SSR goes to\nzero for a large ensemble.",
"arxiv_id": "quant-ph/0309046",
"authors": [
"Howard M. Wiseman",
"Stephen D. Bartlett",
"John A. Vaccaro"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/9789812703002_0047",
"title": "Ferreting out the Fluffy Bunnies: Entanglement constrained by Generalized superselection rules",
"url": "https://arxiv.org/abs/quant-ph/0309046"
},
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