Stellar Representation of Non-Gaussian Quantum States

Area of Science:

• Quantum optics
• Quantum information theory

Background:

• Non-Gaussian properties of quantum states are crucial for advanced quantum technologies.
• The Husimi Q function provides a phase-space representation of quantum states.

Purpose of the Study:

• To introduce and characterize the "stellar hierarchy" of single-mode quantum states.
• To provide an operational method for engineering states within this hierarchy.
• To explore the topological properties and applications of these states.

Main Methods:

• Utilizing the stellar formalism based on the distribution of zeros of the Husimi Q function.
• Defining an infinite hierarchy of states based on the number of Q function zeros.
• Characterizing states by the minimal number of single-photon additions required for their generation.
• Deriving equivalence classes under Gaussian unitary operations.
• Analyzing topological properties with respect to the trace norm.

Main Results:

• An infinite hierarchy of single-mode quantum states, the stellar hierarchy, is established.
• Operational methods for engineering states in the hierarchy using single-photon additions are presented.
• Equivalence classes of states under Gaussian unitary transformations are identified.
• Topological properties of the hierarchy are analyzed.

Conclusions:

• The stellar hierarchy offers a novel framework for classifying and engineering non-Gaussian quantum states.
• The findings have direct implications for advancing non-Gaussian state engineering and continuous-variable quantum computing.