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| related topics |
| {states, state, optimal} |
| {group, space, representation} |
| {equation, function, exp} |
| {entanglement, phys, rev} |
| {state, states, entangled} |
| {qubit, qubits, gate} |
| {level, atom, field} |
| {cos, sin, state} |
| {state, states, coherent} |
| {energy, gaussian, time} |
| {state, algorithm, problem} |
| {operator, operators, space} |
| {time, decoherence, evolution} |
| {classical, space, random} |
| {cavity, atom, atoms} |
| {bell, inequality, local} |
| {phase, path, phys} |
| {measurement, state, measurements} |
| {algorithm, log, probability} |
|
Description of Quantum Entanglement with Nilpotent Polynomials
A. Mandilara, V. M. Akulin, A. V. Smilga, L. Viola
abstract: We propose a general method for introducing extensive characteristics of
quantum entanglement. The method relies on polynomials of nilpotent raising
operators that create entangled states acting on a reference vacuum state. By
introducing the notion of tanglemeter, the logarithm of the state vector
represented in a special canonical form and expressed via polynomials of
nilpotent variables, we show how this description provides a simple criterion
for entanglement as well as a universal method for constructing the invariants
characterizing entanglement. We compare the existing measures and classes of
entanglement with those emerging from our approach. We derive the equation of
motion for the tanglemeter and, in representative examples of up to four-qubit
systems, show how the known classes appear in a natural way within our
framework. We extend our approach to qutrits and higher-dimensional systems,
and make contact with the recently introduced idea of generalized entanglement.
Possible future developments and applications of the method are discussed.
- oai_identifier:
- oai:arXiv.org:quant-ph/0508234
- categories:
- quant-ph
- comments:
- 40 pages, 7 figures, 1 table, submitted for publication. v2: section
II.E has been changed and the Appendix on "Four qubit sl-entanglement
measure" has been removed. There are changes in the notation of section IV.
Typos and language mistakes has been corrected. A figure has been added and a
figure has been replaced. The references have been updated
- doi:
- 10.1103/PhysRevA.74.002331
- arxiv_id:
- quant-ph/0508234
- journal_ref:
- Phys.Rev.A74:002331,2006
- created:
- 2005-08-31
- updated:
- 2006-01-15
Full article ▸
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