Entropy generation in gaussian quantum transformations: Applying the replica method to continuous-variable quantum information theory

Christos N. Gagatsos, Alexandros I. Karanikas, Georgios Kordas, Nicolas J. Cerf

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.

Original languageEnglish (US)
Article number15008
Journalnpj Quantum Information
Volume2
Issue number1
DOIs
StatePublished - 2016
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Statistical and Nonlinear Physics
  • Computer Networks and Communications
  • Computational Theory and Mathematics

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