Quantifying Coherence with Untrusted Devices
arXiv:1812.00844 · doi:10.1002/qute.202000153
Abstract
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. Fundamentally, the superposition property of quantum states, quantified by coherence measures, is a distinct feature to distinguish quantum mechanics from classical theories. In literature, witness and quantification of coherence with trusted devices have been well-studied. However, it remains open whether we can witness and quantify single party coherence with untrusted devices, as it is not clear whether the concept of DI tests exists without a nonlocal setting. In this work, we study DI witness and quantification of coherence with untrusted devices. First, we prove a no-go theorem for a fully DI scenario, as well as a semi DI scenario employing a joint measurement with trusted ancillary states. We then propose a general prepare-and-measure semi DI scheme for witnessing and quantifying the amount of coherence. We show how to quantify the relative entropy and the norm of single party coherence with analytical and numerical methods. As coherence is a fundamental resource for tasks such as quantum random number generation and quantum key distribution, we expect our result may shed light on designing new semi DI quantum cryptographic schemes.
14 pages, 7 figures, comments are welcome!
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