Signatures of nonclassicality in mixed-state quantum computation

Abstract

We investigate signatures of nonclassicality in quantum states, in particular, those involved in the DQC1 model of mixed-state quantum computation [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)]. To do so, we consider two known nonclassicality criteria. The first quantifies disturbance of a quantum state under locally noneffective unitary operations (LNUs), which are local unitaries acting invariantly on a subsystem. The second quantifies measurement-induced disturbance (MID) in the eigenbasis of the reduced density matrices. We study the role of both figures of nonclassicality in the exponential speedup of the deterministic quantum computation with one qubit (DQC1) model and compare them vis-\`a-vis the interpretation provided in terms of quantum discord. In particular, we prove that a nonzero quantum discord implies a nonzero shift under LNUs. We also use the MID measure to study the locking of classical correlations [D. P. DiVincenzo et al., Phys. Rev. Lett. 92, 067902 (2004)] using two mutually unbiased bases (MUBs). We find the MID measure to exactly correspond to the number of locked bits of correlation. For three or more MUBs, it predicts the possibility of superior locking effects.