Entropy production in Gaussian bosonic transformations using the replica method: application to quantum optics

TL;DR

This paper applies the replica method from statistical physics to quantum optics, enabling analytical calculation of entropy production in Gaussian bosonic transformations like two-mode squeezers, revealing new insights into quantum entropy dynamics.

Contribution

It introduces the use of the replica method to analytically compute entropy in Gaussian bosonic transformations, a problem previously considered intractable.

Findings

Derived a simple analytical expression for entropy generated by amplifying a superposition of vacuum and Fock states.

Demonstrated the method's application to two-mode squeezers and optical parametric amplifiers.

Provided new insights into entropy production in Gaussian quantum transformations.

Abstract

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