On the relative character of quantum correlations. A generalized perspective to understand entanglement and discord

G. BELLOMO; A. R. PLASTINO; A. PLASTINO

Buenos Aires

Workshop; International Workshop: What is Quantum Information?; 2015

Entanglement is considered a crucial resource in the performance of quantum information processing, and it is very important to characterize and understand it both qualitatively and quantitatively. However, even today the notion of entanglement ?with its counterpart: separability? is not free of controversy and open problems exist. The first problem arises because there are several complete sets of observables that allow for a similar description of the system, but describe different subsystems or partitions of the whole system (Zanardi 2001; Zanardi, Lidar and Lloyd 2004; Caban et al. 2005; Harshman and Wickramasekara 2007). In algebraic terms, these sets generate the same total observable algebra but induce different subalgebras. Entanglement depends on the substructure of the full system and, therefore, is relative to the selected set of observables. This freedom implies some ambiguity in the notion of entanglement when it is associated to a system and, in order to avoid it, many authors tried to establish a criterion (empirical, operational, etc.) that favors one of all possible descriptions. Yet, the problem can be circumvented by referring to a generalized version of entanglement, where the correlations are defined with respect to a certain subspace of observables, and irrespective of any preferred decomposition of the system into subsystems (Barnum et al. 2004; Viola and Barnum 2007; Derkacz, Gwozdz and Jakobczyk 2012). The same treatment is valid for other types of genuine quantum correlations as discord.This discussion, which we will advance in our work, has profound implications on theoretical and experimental aspects of physics in general, and in quantum information in particular. First, because the relative nature of quantum correlations forces us to rethink the orthodox classical limit of Quantum Mechanics via decoherence (Caponigro and Giannetto 2010; Lychkovskiy 2013; Kastner 2014). The ability to explain the emergence of classical behavior from quantum principles must be investigated, because the picture concerning the resources for information processing becomes more complex, and the potential for important improvements is at hand (Verstraete and Cirac 2003; Bartlett, Rudolph and Spekkens 2007; Thirring et al. 2011; Earman 2014).- Barnum, H., Knill, E., Ortiz, G., Somma, R., & Viola, L. (2004). Phys. Rev. Lett. 92(10), 107902.- Bartlett, S. D., Rudolph, T., & Spekkens, R. W. (2007). Rev. Mod. Phys. 79(2), 555.- Caban, P., Podlaski, K., Rembielinski, J., Smolinski, K. A., & Walczak, Z. (2005). J. Phys. A: Math. Gen. 38(6), 79.- Caponigro, M., & Giannetto, E. (2012). arXiv preprint arXiv:1206.2916.- Derkacz, Ł., Gwóźdź, M., & Jakóbczyk, L. (2012). J. Phys. A: Math. Theor. 45(2), 025302.- Earman, J. (2014). Erkenntnis, 1-35.- Harshman, N. L., & Wickramasekara, S. (2007). Open Systems & Information Dynamics 14(03), 341-351.- Harshman, N. L., & Wickramasekara, S. (2007). Phys. Rev. Lett. 98(8), 080406.- Kastner, R. E. (2014). Stud. Hist. Phil. Sc. Part B: Stud. Hist. Phil. Mod. Phys.- Lychkovskiy, O. (2013). Phys. Rev. A 87(2), 022112.- Thirring, W., Bertlmann, R. A., Köhler, P., & Narnhofer, H. (2011). Eur. Phys. J. D 64(2), 181-196.- Verstraete, F., & Cirac, J. I. (2003). Phys. Rev. Lett. 91(1), 010404.- Viola, L., & Barnum, H. (2007). Philosophy of Quantum Information and Entanglement 16.- Zanardi, P. (2001). Phys. Rev. Lett. 87(7), 077901.- Zanardi, P., Lidar, D. A., & Lloyd, S. (2004). Phys. Rev. Lett. 92(6), 060402.