Certifiability criterion for largescale quantum systems
Abstract
Can one certify the preparation of a coherent, manybody quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of largescale 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 GreenbergerHorneZeilinger states are examples of such asymptotically incertifiable states. More generally, we prove that any socalled 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 almostlinear entropy in the number of qubits. Finally, we show that all unique ground states of local gapped Hamiltonians (in any dimension) are certifiable.
 Publication:

New Journal of Physics
 Pub Date:
 November 2013
 DOI:
 10.1088/13672630/15/11/113011
 arXiv:
 arXiv:1306.0370
 Bibcode:
 2013NJPh...15k3011F
 Keywords:

 Quantum Physics
 EPrint:
 21 pages, 1 figure