Certifiability criterion for large-scale quantum systems

TL;DR

This paper introduces a criterion to evaluate the fragility of large-scale quantum states under noise, distinguishing between certifiable and incertifiable states, with implications for quantum state verification.

Contribution

The authors propose a new certifiability criterion based on state distinguishability after noise, and demonstrate its application to various quantum states including GHZ and ground states.

Findings

GHZ states are asymptotically incertifiable.

Macroscopic superpositions are incertifiable.

Ground states of local gapped Hamiltonians are certifiable.

Abstract

Can one certify the preparation of a coherent, many-body quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of large-scale quantum states which is based on the distinguishability of orthogonal states after the action of very small amounts of noise. States which do not pass this criterion are called asymptotically incertifiable. We show that, if a coherent quantum state is asymptotically incertifiable, there exists an incoherent mixture (with entropy at least log 2) which is experimentally indistinguishable from the initial state. The Greenberger-Horne-Zeilinger states are examples of such asymptotically incertifiable states. More generally, we prove that any so-called macroscopic superposition state is asymptotically incertifiable. We also provide examples of quantum states that are experimentally indistinguishable from highly incoherent mixtures, i.e., with an almost-linear entropy in the number of qubits. Finally we show that all unique ground states of local gapped Hamiltonians (in any dimension) are certifiable.