Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence
- Dipartimento di Fisica 'E. R. Caianiello', Universita degli Studi di Salerno, CNR-Coherentia, Gruppo di Salerno, and INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi (Saudi Arabia) (Italy)
- Institute for Mathematical Sciences, Imperial College, London, London SW7 2PE, United Kingdom and QOLS, Blackett Laboratory, Imperial College, London, Prince Consort Road, London SW7 2BW (United Kingdom)
We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequality constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.
- OSTI ID:
- 20786894
- Journal Information:
- Physical Review. A, Vol. 73, Issue 3; Other Information: DOI: 10.1103/PhysRevA.73.032345; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Bounds on probability of transformations between multipartite pure states
Monogamy inequality in terms of negativity for three-qubit states