Recovering quantum correlations in classical environments without backaction: observation and interpretation

Quantum correlations (entanglement, discord, nonlo-cality) present in a composite quantum system are essential resources for quantum information processing [1, 2]. However, the exploitation of these quantum resources is jeopardized by the detrimental effects of the environment surrounding the quantum system. For instance under Markovian noise, they decay asymptotically or disappear at a finite time [3, 4]. This drawback leads one to look for conditions where quantum correlations can be recovered during the evolution. To this aim non-Markovian noise, arising from strong couplings or structured environments, has been shown to be fundamental because of its memory effects. In fact, in the case of qubits in independent non-Markovian quantum environments, quantum corre- lations exhibit a combination of asymptotic decay with disappearance and revival [2, 5, 6], permitting their partial recovery and thus an extension of their use. Typically, for composite quantum systems within inde- pendent quantum environments, revivals of quantum cor- relations are interpreted as due to correlation exchanges induced by the back-action of non-Markovian quantum environments on the system (flows of quantum informa- tion back and forth from systems to quantum environments) [8-11]. Recently, it has been shown that revivals of quantum correlations may also occur when the envi- ronment is classical, thus unable to store quantum corre- lations, and forbids system-environment back-action [12- 18]. This fact naturally leads to basic issues on the in- terpretation of back-action-free quantum revivals, in par- ticular about: (i) the role of a classical environment in reviving quantum correlations, for instance if it may act as a control system for what operation is applied to the qubits; (ii) the role of collective effects of the environ- ment on the qubits; (iii) the role of the memory effects; (iv) the role of possible system-environment correlations. In this presentation, I first make a brief overview of some theoretical results about revivals of entanglement in classical environments. I describe a model of two nonin- teracting qubits, initially entangled, where only one qubit is subject to a random external classical field (a laser with two random phases) with inhomogeneous broadening in its amplitude [18]. I then report the results of an all- optical experiment that simulates this model and allows us to observe and control revivals of quantum correlations without system-environment back-action [18]. Finally, I discuss about non-Markovianity and provide a possible interpretation showing the role of the classical environ- ment in this phenomenon. The findings so far reveal that the revivals of quantum correlations are a dynamical feature of composite open systems irrespective of the nature, classical or quantum, of the environment. These results introduce the possibil- ity to recover and control, against decoherence, quantum resources even in absence of back-action, without resort- ing to demanding quantum structured environments or quantum error correction procedures and open the way to further studies concerning quantum correlation dynamics in classical environments. [1] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). [2] K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012). [3] T. Yu and J. H. Eberly, Science 323, 598 (2009). [4] J.-S. Xu et al., Nature Commun. 1, 7 (2010). [5] R. Lo Franco, B. Bellomo, S. Maniscalco, and G. Com- pagno, Int. J. Mod. Phys. B 27, 1345053 (2013). [6] J.-S. Xu et al., Phys. Rev. Lett. 104, 100502 (2010). [7] B.-H. Liu et al., Nature Phys. 7, 931 (2011). [8] B. Bellomo, R. Lo Franco, and G. Compagno, Phys. Rev. Lett. 99, 160502 (2007). [9] C. E. Lopez, G. Romero, J. C. Retamal, Phys. Rev. A 81, 062114 (2010). [10] A. Chiuri, C. Greganti, L. Mazzola, M. Paternostro, and P. Mataloni, Sci. Rep. 2, 968 (2012). [11] R. Lo Franco et al., Phys. Scr. T147, 014019 (2012). [12] P. Bordone, F. Buscemi, and C. Benedetti, Fluct. Noise Lett. 11, 1242003 (2012). [13] C. Benedetti et al. Phys. Rev. A 87, 052328 (2013). [14] A. DArrigo, R. Lo Franco, G. Benenti, E. Paladino, and G. Falci, Phys. Scr. T153, 014014 (2013). [15] B. Aaronson, R. Lo Franco, G. Compagno, and G. Adesso, New J. Phys. 15, 093022 (2013). [16] A. DArrigo, R. Lo Franco, G. Benenti, E. Paladino, and G. Falci, arXiv:1207.3294v2 (2014). [17] R. Lo Franco, B. Bellomo, E. Andersson, and G. Com- pagno, Phys. Rev. A 85, 032318 (2012). [18] J.-S. Xu, K. Sun, C.-F. Li, X.-Y. Xu, G.-C. Guo, E. An- dersson, R. Lo Franco and G. Compagno, Nature Commun. 4, 2851 (2013).