On quantum interactive proofs with a laconic prover

arXiv:2609.39495 · quant-ph, cs.CC, cs.CR · Submitted 2026-09-30 · Read on arXiv

quant-ph, cs.CC, cs.CR

Submitted: 2026-09-30

Updated: 2026-10-05

Terminology

• Trace — 48× in this paper · explained in 2 episodes
• Verifier — 41× in this paper · explained in 2 episodes
• BQP — 26× in this paper · explained in 2 episodes
• Steering — 24× in this paper · explained in 2 episodes
• Trace Distance — 22× in this paper · explained in 3 episodes
• Quantum Circuits — 12× in this paper · explained in 2 episodes
• Ancillary Qubits — 8× in this paper · explained in 1 episode
• Accuracy — 6× in this paper · explained in 1 episode
• Quantum State Distinguishability — 6× in this paper
• Block Encoding — 3× in this paper · explained in 4 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Gibbs State — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Error Exponents — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Quantum Entropy Difference Problem — 1× in this paper
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Semidefinite Programming (SDP) — 1× in this paper · explained in 3 episodes

Sources

• Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
• Improvements in Quantum SDP-Solving with Applications
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Properties of Classical and Quantum Jensen-Shannon Divergence
• Quantum Amplitude Amplification and Estimation
• Quantum interactive proofs with short messages
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Designing Optimal Quantum Detectors Via Semidefinite Programming
• Cryptographic Distinguishability Measures for Quantum Mechanical States
• Improved Quantum Algorithms for Fidelity Estimation
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Parallel approximation of min-max problems
• Quantum R'enyi and $f$-divergences from integral representations
• QIP = PSPACE
• Two-message quantum interactive proofs are in PSPACE
• Parallel approximation of non-interactive zero-sum quantum games
• Quantum measurements and the Abelian Stabilizer Problem
• Generalized Quantum Arthur-Merlin Games
• Non-Interactive Quantum Statistical and Perfect Zero-Knowledge
• The operational meaning of min- and max-entropy

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