Achieving perfect completeness for one- and two-message quantum proof systems

arXiv:2609.15926 · quant-ph, cs.CC · Submitted 2026-09-14 · Read on arXiv

quant-ph, cs.CC

Submitted: 2026-09-14

Updated: 2026-09-17

Terminology

• Verifier — 43× in this paper · explained in 2 episodes
• Block Encoding — 25× in this paper · explained in 4 episodes
• Verification — 13× in this paper · explained in 2 episodes
• Ancillary Qubits — 12× in this paper · explained in 1 episode
• Calibration — 12× in this paper · explained in 7 episodes
• Fidelity — 9× in this paper · explained in 2 episodes
• Entanglement — 3× in this paper · explained in 4 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• IEEE Symposium on Foundations of Computer Science — 1× in this paper
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• On Perfect Completeness for QMA
• Limits to black-box amplification in QMA
• Quantum NP - A Survey
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Quantum interactive proofs with short messages
• Eliminating Intermediate Measurements in Space-Bounded Quantum Computation
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Two-message quantum interactive proofs and the quantum separability problem
• QIP = PSPACE
• Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems
• Two-message quantum interactive proofs are in PSPACE
• ${\sf QMA}={\sf QMA}_1$ with an infinite counter
• Using Entanglement in Quantum Multi-Prover Interactive Proofs
• Stronger Methods of Making Quantum Interactive Proofs Perfectly Complete
• Generalized Quantum Arthur-Merlin Games
• Space-bounded quantum interactive proof systems
• Space-bounded quantum state testing via space-efficient quantum singular value transformation
• Quantum Arthur-Merlin Games
• On bit-commitment based quantum coin flipping

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
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity