Efficient Verification of Entangled Measurements with Local States
Abstract Overview
This paper develops a framework for quantum measurement verification (QMV) that uses only local product-state preparations to test entangled von Neumann measurements. The core formulation defines verification through the worst-case passing probability against faulty POVMs with bounded measurement fidelity, and derives the corresponding sample complexity. A central theoretical result shows that when the target measurement is locally transitive and irreducible, symmetry reduces locality-constrained QMV to quantum state verification of a single representative basis state. The framework is then instantiated for generalized Bell measurements, single-parameter two-qubit measurements, elegant joint measurements, and stabilizer-state-induced measurements, with explicit local protocols and homogeneous verification operators.
Novelty
The distinctive contribution is a symmetry-based reduction that converts a difficult locality-constrained measurement-verification problem into a standard state-verification problem for one basis element under stated symmetry conditions. The work also provides explicit local-state protocols for several important entangled measurements and connects homogeneous QMV protocols to direct measurement-fidelity estimation from pass frequencies.
Results
The paper derives closed-form verification operators, worst-case passing probabilities, and sample complexities for several measurement families using only local test states. For generalized Bell measurements in prime dimension, the local protocol achieves passing probability 1 - d/(d+1)·ε, implying only a constant-factor overhead relative to the unconstrained optimum; analogous explicit formulas are given for the single-parameter two-qubit, elegant joint, and stabilizer-induced cases. The authors further show that homogeneous protocols allow direct estimation of measurement fidelity from observed pass frequencies, although with estimation scaling that is quadratically worse than verification scaling.
Key Points
- A theorem shows that for locally transitive and irreducible von Neumann measurements, symmetric local QMV reduces to quantum state verification of a single representative basis state.
- The framework yields explicit homogeneous local verification protocols for generalized Bell, single-parameter two-qubit, elegant joint, and stabilizer-state-induced measurements, including closed-form success probabilities and sample complexities.
- For generalized Bell measurements, locality causes only a constant-factor verification overhead compared with the globally optimal unconstrained protocol, and homogeneous protocols also support direct fidelity estimation from pass statistics.