Unified framework to determine Gaussian states in continuous variable systems

TL;DR

This paper presents a practical method to determine the covariance matrix of any n-mode Gaussian state in continuous variable quantum systems by measuring total phases after specific metaplectic evolutions, using an ancilla qubit.

Contribution

It introduces a novel, experimentally feasible approach to fully characterize Gaussian states via phase measurements with minimal operations and an ancilla qubit.

Findings

Method determines all covariance matrix elements with simple evolutions.

Uses an ancilla qubit to measure phases, simplifying experimental procedures.

Applicable to current continuous variable quantum systems.

Abstract

Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the reduced states in a given bipartition of a multipartite quantum system bears information on the entanglement in such bipartition. For Gaussian states, the reduced states are also Gaussian, so there determination requires essentially the experimental determination of their covariance matrix. Here, we develop strategies to determine the covariance matrix of an arbitrary n-mode bosonic Gaussian state through measurement of the total phase acquired when appropriate metaplectic evolutions, associated with quadratic Hamiltonians, are applied. Simply one-mode metaplectic evolutions, such rotations, squeezing and shear transformations, in addition to a single two-mode rotation, allows to determine all the covariance matrix elements of a n-mode bosonic system. All the single-mode metaplectic evolutions are applied conditionally to a state in which an ancilla qubit is entangled with the n-mode system. The ancillary system provides, after measurement, the value of the total phase of each evolution. The proposed method is experimentally friendly to be implemented in the most currently used continuous variable systems.