Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses

Abstract

Reliable and well-characterized quantum resources are indispensable ingredients in quantum information processing. Typically, in a realistic characterization of these resources, apparatuses come with intrinsic uncertainties that can manifest themselves in the form of systematic errors. While systematic errors are generally accounted for through careful calibration, the effect of remaining imperfections on the characterization of quantum resources has been largely overlooked in the literature. In this paper, we investigate the effect of systematic errors that arise from imperfect alignment of measurement bases --- an error that can conceivably take place due to the limited controlability of measurement devices. We show that characterization of quantum resources using quantum state tomography or entanglement witnesses can be undermined with an amount of such imprecision that is not uncommon in laboratories. Curiously, for quantum state tomography, we find that having entanglement can help to reduce the susceptibility to this kind of error. We also briefly discuss how a given entanglement witness can be modified to incorporate the effect of such errors.

13 pages, 9 figures. Key results moved from Appendices to main text, proofs strengthened, figures added and text corrected to aid readability

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• Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames
• Effects of preparation and measurement misalignments on the security of the BB84 quantum key distribution protocol
• Simultaneous Estimation of Dimension, States and Measurements: Computation of representative density matrices and POVMs