A theory of nonclassicality and athermality in continuous-variable quantum systems
A resource theory in quantum information studies a quantum mechanical resource (e.g. entanglement) by characterizing the operational restrictions that the resource helps alleviate (e.g. local operations). In these works, we apply this approach to resources on continuous-variable (CV) systems comprising bosonic modes. In , we develop the resource theory of nonclassicality (as defined by negative values in the Glauber–Sudarshan representation), where the relevant operational restriction is to networks of passive linear elements and measurements with feed forward. We derive a host of results on the manipulation of nonclassicality resource under such operations, including: new nonclassicality measures based on quadrature variances and quantum Fisher information of displacements; fundamental constraints on nonclassicality concentration; no-go results on the concentration of squeezing; and a complete hierarchy of nonclassicality for single-mode Gaussian states. In , we formulate a resource theory of thermodynamic inequilibrium (“athermality”) on bosonic CV systems under a restriction to passive linear elements and strictly thermal ancillary modes, which we call Gaussian thermal operations (GTO). We find several new “second laws of thermodynamics” under GTO, some in terms of the phase-space displacements, and others in terms of the eigenvalues and symplectic eigenvalues of the phase-space covariance matrix. The latter correspond directly to impossibility of athermality concentration, and together with the former, imply a monotonous deterioration under GTO of the signal-to-noise ratio in phase-space displacement information.
 Benjamin Yadin, Felix C. Binder, Jayne Thompson, Varun Narasimhachar, Mile Gu, and M. S. Kim. arXiv:1804.10190 (to appear in Phys. Rev. X)
 Varun Narasimhachar, Felix C. Binder, Jayne Thompson, Benjamin Yadin, Syed M. Assad, and Mile Gu. In preparation.