Classical description of bosonic quantum fields in terms of the reduced-state-of-the-field framework

We discuss compatibility between various quantum aspects of bosonic fields, relevant for quantum optics and quantum thermodynamics, and the mesoscopic formalism of reduced state of the field (RSF). In particular, we derive exact conditions under which Gaussian and Bogoliubov-type evolutions can be cast into the RSF framework. In that regard, special emphasis is put on Gaussian thermal operations. To strengthen the link between the RSF formalism and the notion of classicality for bosonic quantum fields, we prove that RSF contains no information about entanglement in two-mode Gaussian states. For the same purpose, we show that the entropic characterisation of RSF by means of the von Neumann entropy is qualitatively the same as its description based on the Wehrl entropy. Our findings help bridge the conceptual gap between quantum and classical mechanics.

Dissipative evolution of covariance matrix beyond quadratic order

The covariance matrix contains the complete information about the second-order expectation values of the mode quadratures (position and momentum operators) of the system. Due to its prominence in studies of continuous variable systems, most significantly Gaussian states, special emphasis is put on time evolution models that result in self-contained equations for the covariance matrix. So far, despite not being explicitly implied by this requirement, virtually all such models assume a so-called quadratic, or second-order case, in which the generator of the evolution is at most second-order in the mode quadratures. Here, we provide an explicit model of covariance matrix evolution of infinite order. Furthermore, we derive the solution, including stationary states, for a large subclass of proposed evolutions. Our findings challenge the contemporary understanding of covariance matrix dynamics and may give rise to new methods and improvements in quantum technologies employing continuous variable systems.

Stabilizing entanglement in two-mode Gaussian states

We analyze the stabilizability of entangled two-mode Gaussian states in three benchmark dissipative models: local damping, dissipators engineered to preserve two-mode squeezed states, and cascaded oscillators. In the first two models, we determine principal upper bounds on the stabilizable entanglement, while in the last model, arbitrary amounts of entanglement can be stabilized. All three models exhibit a tradeoff between state entanglement and purity in the entanglement maximizing limit. Our results are derived from the Hamiltonian-independent stabilizability conditions for Gaussian systems. Here, we sharpen these conditions with respect to their applicability.

Entangling power of multipartite unitary gates

We study the entangling properties of multipartite unitary gates with respect to the measure of entanglement called one-tangle. Putting special emphasis on the case of three parties, we derive an analytical expression for the entangling power of an $n$-partite gate as an explicit function of the gate, linking the entangling power of gates acting on $n$-partite Hilbert space of dimension $d_1 ldots d_n$ to the entanglement of pure states in the Hilbert space of dimension $(d_1 ldots d_n)^2$. Furthermore, we evaluate its mean value averaged over the unitary and orthogonal groups, analyze the maximal entangling power and relate it to the absolutely maximally entangled (AME) states of a system with $2n$ parties. Finally, we provide a detailed analysis of the entangling properties of three-qubit unitary and orthogonal gates.