arXiv subjects

Piotr Badziąg

Publications and source records attributed to Piotr Badziąg.

3 recordsLinked to original sources

arXiv2018

Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality

We prove that as conjectured by Ac\'ın et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant Bell inequality. This suggests a surprising connection between maximal entanglement, complete sets of mutually unbiased bases, and elements of symmetric informationally complete positive operator-valued measures, on one side, and the optimal way of certifying maximal randomness, on the other.

quant-ph↗

arXiv2017

Self-testing properties of Gisin's elegant Bell inequality

An experiment in which the Clauser-Horne-Shimony-Holt inequality is maximally violated is self-testing (i.e., it certifies in a device-independent way both the state and the measurements). We prove that an experiment maximally violating Gisin's elegant Bell inequality is not similarly self-testing. The reason can be traced back to the problem of distinguishing an operator from its complex conjugate. We provide a complete and explicit characterization of all scenarios in which the elegant Bell inequality is maximally violated. This enables us to see exactly how the problem plays out.

quant-ph↗

arXiv2013

Separability in terms of a single entanglement witness

The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state \varrho is separable if and only if a specially constructed entanglement witness W_{\varrho} is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the conceptual aspect of the separability problem and rises some questions about properties of positive maps.

quant-ph↗