Universal and Efficient Quantum State Verification via Schmidt Decomposition and Mutually Unbiased Bases

TL;DR

This paper introduces a universal, efficient protocol for verifying multipartite quantum states using local measurements, with a sample complexity bound independent of local dimensions, applicable even in adversarial scenarios.

Contribution

It presents a novel verification protocol based on Schmidt decomposition and mutually unbiased bases, establishing a universal sample complexity bound and simpler variants without Schmidt decomposition.

Findings

Haar-random pure states can be verified with constant sample cost

The protocol's sample complexity is independent of local dimensions

Simpler variants achieve high efficiency without Schmidt decomposition

Abstract

Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify arbitrary multipartite pure quantum states using adaptive local projective measurements. Moreover, we establish a universal upper bound on the sample complexity that is independent of the local dimensions. Numerical calculations further indicate that Haar-random pure states can be verified with a constant sample cost, irrespective of the qudit number and local dimensions, even in the adversarial scenario in which the source cannot be trusted. As alternatives, we provide several simpler variants that can achieve similar high efficiencies without using Schmidt decomposition. The simplest variant consists of only two distinct tests.