Quantum non-Gaussianity and secure quantum communication

Abstract

No-cloning theorem, a profound fundamental principle of quantum mechanics, also provides a crucial practical basis for secure quantum communication. The security of communication can be ultimately guaranteed if the output fidelity via communication channel is above the no-cloning bound (NCB). In quantum communications using continuous-variable (CV) systems, Gaussian states, more specifically, coherent states have been widely studied as inputs, but less is known for non-Gaussian states. We aim at exploring quantum communication covering CV states comprehensively with distinct sets of unknown states properly defined. Our main results here are (i) to establish the NCB for a broad class of quantum non-Gaussian states including Fock states, their superpositions and Schrodinger-cat states and (ii) to examine the relation between NCB and quantum non-Gaussianity (QNG). We find that NCB typically decreases with QNG. Remarkably, this does not mean that quantum non-Gaussian states are less demanding for secure communication. By extending our study to mixed-state inputs, we demonstrate that QNG specifically in terms of Wigner negativity requires more resources to achieve output fidelity above NCB in CV teleportation. The more non-Gaussian, the harder to achieve secure communication, which can have crucial implications for CV quantum communications.

Quantification of Wigner Negativity Remotely Generated via Einstein-Podolsky-Rosen Steering

“…These protocols come with the advantage of deterministically producing resource states and being analytically tractable due to the Gaussian properties of the states. However, non-Gaussian states and operations have irreplaceable advantages in several CV protocols [6], such as entanglement distillation [7,8], error correction [9], secure quantum communication [10], and the verification of Bell nonlocality [11]. Considerable progresses in controllable generation of multimode non-Gaussian states have been made in recent experiments [12,13], which also provide support for the implementation of universal CV quantum computation in the long term [14].…”

Entropic nonclassicality and quantum non-Gaussianity tests via beam splitting

“…For instance, our approach can be generalized to adopt Renyi entropies beyond Shannon entropy. It will also be interesting to examine how these entropic criteria can be useful for critical assessment of quantum tasks using continuous variables in relation to QNG 62 .…”

Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state

“…Therefore, one can also use the quasidistribution functions to study non-Gaussianity both qualitatively and quantitatively [92]. Non-Gaussian states are also found useful in a set of secure quantum communication schemes [51,52,93].…”