Complexity of quantum tomography from genuine non-Gaussian entanglement

Area of Science:

• Quantum Information Science
• Quantum Optics
• Quantum Computing

Background:

• Quantum state tomography is crucial for characterizing quantum systems.
• Traditional methods require exponentially many state copies, limiting scalability.
• Bosonic systems present unique challenges due to complex correlations.

Purpose of the Study:

• To develop an efficient quantum state tomography protocol for bosonic systems.
• To define a new class of states, Gaussian-entanglable (GE) states, amenable to efficient tomography.
• To quantify the tomography overhead for states beyond the GE class.

Main Methods:

• Definition of Gaussian-entanglable (GE) states based on generalized interference.
• Development of a protocol using Gaussian unitaries, local tomography, and classical post-processing.
• Introduction of an operational monotone to characterize tomography complexity.

Main Results:

• Any pure GE state of m modes can be learned efficiently using poly(m) copies.
• Boson-sampling states can be learned without Gaussian unitaries.
• An operational monotone precisely quantifies the exponential tomography overhead for non-GE states.
• Deterministic generation of NOON states (N ≥ 3) via two-mode interference is shown to be impossible.

Conclusions:

• Efficient quantum state tomography is achievable for a significant class of bosonic states (GE states).
• The GE state definition and associated tomography protocol offer a pathway to scalable quantum information processing.
• The study provides a clear metric for tomography complexity and highlights limitations in generating certain quantum states.