dorsal/arxiv
View SchemaContinuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
| Authors | Gerardo Adesso, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410050 |
| URL | https://arxiv.org/abs/quant-ph/0410050 |
| DOI | 10.1088/1367-2630/8/1/015 |
| Journal | New J. Phys. 8, 15 (2006) |
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.
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"abstract": "For continuous-variable systems, we introduce a measure of entanglement, the\ncontinuous variable tangle ({\\em contangle}), with the purpose of quantifying\nthe distributed (shared) entanglement in multimode, multipartite Gaussian\nstates. This is achieved by a proper convex roof extension of the squared\nlogarithmic negativity. We prove that the contangle satisfies the\nCoffman-Kundu-Wootters monogamy inequality in all three--mode Gaussian states,\nand in all fully symmetric $N$--mode Gaussian states, for arbitrary $N$. For\nthree--mode pure states we prove that the residual entanglement is a genuine\ntripartite entanglement monotone under Gaussian local operations and classical\ncommunication. We show that pure, symmetric three--mode Gaussian states allow a\npromiscuous entanglement sharing, having both maximum tripartite residual\nentanglement and maximum couplewise entanglement between any pair of modes.\nThese states are thus simultaneous continuous-variable analogs of both the GHZ\nand the $W$ states of three qubits: in continuous-variable systems monogamy\ndoes not prevent promiscuity, and the inequivalence between different classes\nof maximally entangled states, holding for systems of three or more qubits, is\nremoved.",
"arxiv_id": "quant-ph/0410050",
"authors": [
"Gerardo Adesso",
"Fabrizio Illuminati"
],
"categories": [
"quant-ph",
"cond-mat.other",
"math-ph",
"math.MP",
"physics.optics"
],
"doi": "10.1088/1367-2630/8/1/015",
"journal_ref": "New J. Phys. 8, 15 (2006)",
"title": "Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems",
"url": "https://arxiv.org/abs/quant-ph/0410050"
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