|
| related topics |
| {state, states, entangled} |
| {alice, bob, state} |
| {spin, pulse, spins} |
| {group, space, representation} |
| {information, entropy, channel} |
| {field, particle, equation} |
| {bell, inequality, local} |
| {cavity, atom, atoms} |
| {cos, sin, state} |
| {temperature, thermal, energy} |
| {entanglement, phys, rev} |
| {measurement, state, measurements} |
| {level, atom, field} |
|
Entanglement and Symmetry: A Case Study in Superselection Rules,
Reference Frames, and Beyond
S. J. Jones, H. M. Wiseman, S. D. Bartlett, J. A. Vaccaro, D. T. Pope
abstract: This paper concentrates on a particular example of a constraint imposed by
superselection rules (SSRs): that which applies when the parties (Alice and
Bob) cannot distinguish among certain quantum objects they have. This arises
naturally in the context of ensemble quantum information processing such as in
liquid NMR. We discuss how a SSR for the symmetric group can be applied, and
show how the extractable entanglement can be calculated analytically in certain
cases, with a maximum bipartite entanglement in an ensemble of N Bell-state
pairs scaling as log(N) as N goes to infinity . We discuss the apparent
disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement
for other sorts of superselection rules, and show that the disparity disappears
when the correct notion of applying the symmetric group SSR to multiple copies
is used. Next we discuss reference frames in the context of this SSR, showing
the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502
(2004)]. The action of a reference frame can be regarded as the analog of
activation in mixed-state entanglement. We also discuss the analog of
distillation: there exist states such that one copy can act as an imperfect
reference frame for another copy. Finally we present an example of a stronger
operational constraint, that operations must be non-collective as well as
symmetric. Even under this stronger constraint we nevertheless show that
Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble
of N Bell-state pairs no matter how large N is. This last work is a
generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].
- oai_identifier:
- oai:arXiv.org:quant-ph/0608056
- categories:
- quant-ph
- comments:
- 16 pages, 6 figures. v2 updated version published in Phys Rev A
- doi:
- 10.1103/PhysRevA.74.062313
- arxiv_id:
- quant-ph/0608056
- journal_ref:
- Phys. Rev. A 74, 062313 (2006)
- created:
- 2006-08-07
- updated:
- 2006-12-20
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