Estimating Coherence Measures with Untrusted Devices

Abstract

AbstractThe superposition of quantum states, quantified by coherence, is a fundamental feature to distinguish quantum mechanics from classical theories. Estimations of coherence with perfectly characterised devices have been well‐studied. However, imperfections or malfunctions of realistic measurement devices might nullify the characterization. Device‐independent (DI) tests allow to witness and quantify the quantum feature of a system, such as entanglement, without trusting the implementation devices. Although DI test is a powerful tool in many quantum information tasks, it generally requires nonlocal settings. Little is known if single party coherence can be witnessed and estimated via untrusted devices. In this work, coherence witnesses and estimations with untrusted devices are systematically studied. First, a no‐go theorem for detecting existences of single party coherence via a DI or semi DI means is proven. A general prepare‐and‐measure semi DI scheme for witnessing and estimating the amount of coherence is then proposed. How to estimate the relative entropy and the l1 norm of single party coherence with analytical and numerical approaches is shown. As coherence is an essential resource for tasks such as quantum random number generation and quantum key distribution, it is expected that this result may shed light on designing new quantum cryptographic schemes.