Quantum Coherent State Transform on Continuous-Variable Systems

TL;DR

The paper introduces the quantum coherent state transform (QCST), a new framework for efficiently manipulating and measuring continuous-variable quantum states, enabling precise estimation, calibration, and tomography with broad applications.

Contribution

It presents the first implementation framework for QCST in CV systems, allowing efficient state estimation, calibration, and state transfer, expanding the toolkit for CV quantum information processing.

Findings

Enables minimum-uncertainty estimation of coherent states with a single copy.

Allows Gaussian state parameter estimation and gate calibration.

Facilitates Husimi Q-function tomography for non-Gaussian states.

Abstract

While continuous-variable (CV) quantum systems are believed to be more efficient for quantum sensing and metrology than their discrete-variable (DV) counterparts due to the infinite spectrum of their native operators, our toolkit of manipulating CV systems is still limited. We introduce the quantum coherent state transform~(QCST) and a framework for implementing it in CV quantum systems with two ancilla CV states and six two-mode SUM gates. Measurement of the resulting quantum state under the momentum eigenbasis is equivalent to a positive operator-valued measure (POVM) with elements $\left\{\frac{1}{\pi} \left|\alpha\right\rangle \left\langle\alpha\right| \right\}_{\alpha \in \mathbb{C}}$ , which provides an efficient way to learn the original CV state. Our protocol makes it possible to estimate the coherent state parameter within minimum-uncertainty precision using a single copy of the state, which finds applications in single-shot gate calibration of beam splitter and rotation gates to arbitrary precision. With repeated runs of our protocol, one can also estimate the parameters of any Gaussian state, which helps to calibrate other Gaussian gates, such as squeezing. For non-Gaussian states, our protocols can be used to perform Husimi Q-function tomography efficiently. With DV systems as ancilla instead, we can realize QCST approximately, which can be used to transfer CV states to DV states and back. The simplicity and broad applicability of the quantum coherent state transform make it an essential tool in continuous-variable quantum information science and engineering.