|
| related topics |
| {state, states, entangled} |
| {entanglement, phys, rev} |
| {energy, gaussian, time} |
| {state, states, coherent} |
| {bell, inequality, local} |
| {information, entropy, channel} |
|
Continuous variable tangle, monogamy inequality, and entanglement
sharing in Gaussian states of continuous variable systems
Gerardo Adesso, Fabrizio Illuminati
abstract: For continuous-variable systems, we introduce a measure of entanglement, the
continuous variable tangle ({\em contangle}), with the purpose of quantifying
the distributed (shared) entanglement in multimode, multipartite Gaussian
states. This is achieved by a proper convex roof extension of the squared
logarithmic negativity. We prove that the contangle satisfies the
Coffman-Kundu-Wootters monogamy inequality in all three--mode Gaussian states,
and in all fully symmetric $N$--mode Gaussian states, for arbitrary $N$. For
three--mode pure states we prove that the residual entanglement is a genuine
tripartite entanglement monotone under Gaussian local operations and classical
communication. We show that pure, symmetric three--mode Gaussian states allow a
promiscuous entanglement sharing, having both maximum tripartite residual
entanglement and maximum couplewise entanglement between any pair of modes.
These states are thus simultaneous continuous-variable analogs of both the GHZ
and the $W$ states of three qubits: in continuous-variable systems monogamy
does not prevent promiscuity, and the inequivalence between different classes
of maximally entangled states, holding for systems of three or more qubits, is
removed.
- oai_identifier:
- oai:arXiv.org:quant-ph/0410050
- categories:
- quant-ph cond-mat.other math-ph math.MP physics.optics
- comments:
- 13 pages, 1 figure. Replaced with published version
- doi:
- 10.1088/1367-2630/8/1/015
- arxiv_id:
- quant-ph/0410050
- journal_ref:
- New J. Phys. 8, 15 (2006)
- created:
- 2004-10-06
- updated:
- 2006-02-02
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