Efficient multimode Wigner tomography

TL;DR

This paper introduces a polynomial-scaling quantum state tomography method for multimode systems, enabling efficient characterization of complex states like entangled W states across multiple bosonic modes.

Contribution

The authors develop a scalable Wigner tomography technique that reduces measurement complexity from exponential to polynomial in the number of modes, demonstrated on up to 4 modes.

Findings

Successfully reconstructed multimode entangled states up to 4 modes.

Achieved improved efficiency over traditional methods for 3 and 4 modes.

Theoretically scalable to higher mode numbers with greater efficiency.

Abstract

Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially in both computational and experimental measurement requirement, which becomes prohibitive as the state size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with subspace size, and thus mode number, for states that can be expressed within such a subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.