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| related topics |
| {entanglement, phys, rev} |
| {let, theorem, proof} |
| {states, state, optimal} |
| {state, algorithm, problem} |
| {alice, bob, state} |
| {cos, sin, state} |
| {error, code, errors} |
| {operator, operators, space} |
|
Entangling Power of Permutations
Lieven Clarisse, Sibasish Ghosh, Simone Severini, Anthony Sudbery
abstract: The notion of entangling power of unitary matrices was introduced by Zanardi,
Zalka and Faoro [PRA, 62, 030301]. We study the entangling power of
permutations, given in terms of a combinatorial formula. We show that the
permutation matrices with zero entangling power are, up to local unitaries, the
identity and the swap. We construct the permutations with the minimum nonzero
entangling power for every dimension. With the use of orthogonal latin squares,
we construct the permutations with the maximum entangling power for every
dimension. Moreover, we show that the value obtained is maximum over all
unitaries of the same dimension, with possible exception for 36. Our result
enables us to construct generic examples of 4-qudits maximally entangled states
for all dimensions except for 2 and 6. We numerically classify, according to
their entangling power, the permutation matrices of dimension 4 and 9, and we
give some estimates for higher dimensions.
- oai_identifier:
- oai:arXiv.org:quant-ph/0502040
- categories:
- quant-ph
- comments:
- 8 pages. We have deleted the appendix. We have pointed out that our
result enables to construct generic examples of 4-qudits maximally entangled
states for all dimensions except for 2 and 6. Accepted for publication in
Phys. Rev. A
- doi:
- 10.1103/PhysRevA.72.012314
- arxiv_id:
- quant-ph/0502040
- journal_ref:
- Phys. Rev. A 72, 012314 (2005)
- created:
- 2005-02-07
- updated:
- 2005-04-11
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