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Updated: Feb 1, 2026
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
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Matrix-Product Entanglement Characterizing the Optimality of State-Preparation Quantum Circuits
Shuo Qi1,2, Wen-Jun Li3, Gang Su4,5
1Capital Normal University, Center for Quantum Physics and Intelligent Sciences, Department of Physics, Beijing 10048, China.
Physical Review Letters
|January 30, 2026
Summary
We introduce χ-specified matrix product entanglement (χ-MPE), a new measure for multipartite entanglement. It assesses quantum circuit optimality for state preparation by analyzing scaling behaviors related to fidelity and circuit depth.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
- Quantum Many-Body Systems
Background:
- Multipartite entanglement is crucial for understanding complex quantum phenomena.
- Conventional bipartite entanglement measures fall short for these systems.
- Matrix product states (MPS) offer a powerful representation for quantum states.
Purpose of the Study:
- To propose a novel class of multipartite entanglement measures.
- To enable characterization of quantum circuit optimality for state preparation.
- To leverage the MPS representation for entanglement quantification.
Main Methods:
- Definition of χ-specified matrix product entanglement (χ-MPE) measures.
- Quantification based on minimal distance to MPS manifolds with specified virtual bond dimensions (χ).
- Analysis of scaling behaviors of χ-MPE with negative logarithmic fidelity (F) and circuit depth (D).
Main Results:
- Demonstrated superlinear, linear, and sublinear scaling of χ-MPE with fidelity.
- Correlated these scaling behaviors with excessive, optimal, and insufficient circuit depths.
- Proved that H_{χ=2} is equivalent to H_{D=1}, where H denotes state manifolds.
Conclusions:
- χ-MPE provides a robust tool for assessing quantum circuit performance.
- Tensor networks are established as versatile tools for developing entanglement measures.
- The MPS-based approach is extendable to other tensor network Ansätze for circuit optimality assessment.
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