Deterministic Photonic Entanglement Arising from Non-Abelian Quantum Holonomy.

Area of Science:

• Quantum Information Science
• Photonics
• Quantum Optics

Background:

• Deterministic photon entanglement is crucial for quantum information processing but remains a significant challenge.
• Previous research has explored various methods, but achieving high fidelity and control has been elusive.

Purpose of the Study:

• To devise a protocol for creating and manipulating highly entangled photon states.
• To demonstrate deterministic entanglement of N-dimensional quantum systems using photonic platforms.
• To establish a connection between quantum holonomy and irreducible representations for entanglement.

Main Methods:

• Utilizing an on-chip photonic system capable of three-dimensional, non-Abelian quantum holonomy.
• Analyzing matrix representations of unitary quantum holonomy within energy-degenerate subspaces.
• Connecting quantum holonomy to irreducible representations of rotation operators for N-dimensional systems.

Main Results:

• The protocol enables the creation of highly entangled superpositions of well-controlled light states.
• Calculations show that some entangled states are maximally entangled, "volume-law" states.
• The approach allows for deterministic entanglement of two arbitrarily high, N-dimensional quantum systems.

Conclusions:

• The developed protocol offers a pathway for deterministic quantum information processing with light.
• Entanglement generated can be distilled and purified for quantum science applications.
• The method deterministically entangles distinguishable, individually accessible photonic modes.