Tensor-Network Algorithm Enables Efficient Trace Norm Calculations for Many-Body Quantum Systems
By
[Submitted on 10 Jun 2026]
Plain bagel done well. Pleasantly substantive.
Summary
This paper introduces a tensor-network algorithm for efficiently estimating trace norms in many-body quantum systems, which are fundamental to quantum information theory but computationally expensive due to the need to diagonalize exponentially large operators. The method combines Zolotarev's rational approximation to the sign function with a variational formulation solved using a density-matrix-renormalization-group-like algorithm. The approach is systematically improvable and demonstrates controlled trace-norm calculations for entanglement negativity, quantum fidelity, and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches. This establishes trace-norm-based quantities as practical tensor-network observables for studying quantum information in mixed states.
Key quotes
· 5 pulledTrace norms are fundamental to quantum information theory, yet in many-body systems their evaluation remains a major computational bottleneck, as it generally requires diagonalizing exponentially large operators.
Here, we overcome this bottleneck by introducing a controlled tensor-network algorithm for estimating the trace norm of matrix product operators without full diagonalization.
The resulting approximation is systematically improvable, with its accuracy controlled by the rational approximation parameters and the spectral weight near zero.
Beyond the reach of exact diagonalization, we demonstrate controlled trace-norm calculations for entanglement negativity, quantum fidelity and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches.
Our results establish trace-norm-based quantities as practical tensor-network observables, opening a route toward tensor-network studies of quantum information in mixed states.
