Local Test for Unitarily Invariant Properties of Bipartite Quantum States

arXiv:2404.04599 · quant-ph, cs.CC, cs.IT, math.IT · Submitted 2024-04-06 · Read on arXiv

quant-ph, cs.CC, cs.IT, math.IT

Submitted: 2024-04-06

Updated: 2026-09-15

Comments: 56 pages. [v2]: extended testers with parameterized completeness and soundness, added new lower bounds for testing the bond dimension of matrix product states (MPS), and improved the lower bounds for testing Schmidt rank; [v3] and [v4]: minor revision

Journal ref: IEEE Transactions on Information Theory, 72(10): 7578-7603, 2026

DOI: 10.1109/TIT.2026.3697790

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Entanglement — 89× in this paper · explained in 3 episodes
• Sample Complexity — 76× in this paper · explained in 15 episodes
• Entanglement Entropy — 37× in this paper · explained in 2 episodes
• Trace — 22× in this paper · explained in 2 episodes
• Trace Distance — 17× in this paper · explained in 3 episodes
• Hilbert Space — 11× in this paper · explained in 2 episodes
• Query Complexity — 10× in this paper · explained in 2 episodes
• Area Law — 7× in this paper · explained in 1 episode
• Generalization — 4× in this paper · explained in 13 episodes
• Verification — 4× in this paper · explained in 2 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Fidelity — 2× in this paper · explained in 2 episodes
• Frustration — 2× in this paper · explained in 2 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Linear Combination of Unitaries — 1× in this paper
• Quantum Physics — 1× in this paper · explained in 10 episodes

Sources

• Complexity Theory for Quantum Promise Problems
• A List of Complexity Bounds for Property Testing by Quantum Sample-to-Query Lifting
• Quantum channel tomography and estimation by local test
• Random purification channel made simple
• Random Stinespring superchannel: converting channel queries into dilation isometry queries
• The Church of the Symmetric Subspace
• Exponential Separations between Quantum Learning with and without Purification
• Test of Purity by LOCC
• Optimal learning of quantum channels in diamond distance
• Random purification channel for passive Gaussian bosons
• Mixed state tomography reduces to pure state tomography
• Conjugate queries can help
• A random purification channel for arbitrary symmetries with applications to fermions and bosons
• Random dilation superchannel

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• A quasiparticle-protected superconducting qubit
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians