Characterizing Entanglement and Quantum Correlations by Jordi Tura i Brugués

By Jordi Tura i Brugués

This thesis specializes in the learn and characterization of entanglement and nonlocal correlations limited lower than symmetries. It contains unique effects in addition to special tools and causes for a couple of diverse threads of study: confident partial transpose (PPT) entanglement within the symmetric states; a unique, experimentally pleasant technique to become aware of nonlocal correlations in many-body structures; the non-equivalence among entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations represent basic assets for quantum details processing, as they enable novel projects which are differently most unlikely in a classical situation. although, their elusive characterization continues to be a principal challenge in quantum info thought. the most the reason is, this type of primary factor continues to be an impressive problem lies within the exponential progress in complexity of the Hilbert area in addition to the distance of multipartite correlations. actual structures of curiosity, nonetheless, demonstrate symmetries that may be exploited to minimize this complexity, beginning the prospect that a few of these questions develop into tractable for such systems.

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97(17), 170409 (2006). 170409 [Bru+14] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, S. Wehner, Bell nonlocality. Rev. Mod. Phys. 86(2), 419–478 (2014). 419 [CKW00] V. Coffman, J. K. Wootters, Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000). 052306 [CR12] C. Roger, R. Renato, Free randomness can be amplified. Nat. Phys. 8(6), 450–453 (2012). 1038/nphys2300. H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99–110 (1954). 99 10 1 Introduction [Eck+02] K. Eckert, J.

2), we also obtain a positive state (i) pi ρ(i) 0. 2) hence it must be entangled. 6) for all positive, but not completely positive, maps [HHH96]. In practice, one cannot check this condition for all , but there are maps that very well approximate Dsep . upper bound s ≤ d12 d22 , stems from Carathodory’s theorem [Car11]: Any state expressed as a convex combination like in Eq. 2) can be re-expressed as another convex combination of no more than dim D(HAB ) terms, as D(HAB ) can be embedded into the -vector space of d1 d2 × d1 d2 Hermitian matrices, which has dimension d12 d22 .

Mod. Phys. 86(2), 419–478 (2014). 419 [CKW00] V. Coffman, J. K. Wootters, Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000). 052306 [CR12] C. Roger, R. Renato, Free randomness can be amplified. Nat. Phys. 8(6), 450–453 (2012). 1038/nphys2300. H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99–110 (1954). 99 10 1 Introduction [Eck+02] K. Eckert, J. Schliemann, D. Bruß, M. Lewenstein, Quantum correlations in systems of indistinguishable particles. Ann. Phys. 299(1), 88–127 (2002).

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