Piotr Badziag

Experimentally Friendly Geometrical Criteria for Entanglement

A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.

Simple Hardy-Like Proof of Quantum Contextuality

Contextuality and nonlocality are two fundamental properties of nature. Hardys proof is considered the simplest proof of nonlocality and can also be seen as a particular violation of the simplest Bell inequality. A fundamental question is: Which is the simplest proof of contextuality? We show that there is a Hardy-like proof of contextuality that can also be seen as a particular violation of the simplest noncontextuality inequality. Interestingly, this new proof connects this inequality with the proof of the Kochen-Specker theorem, providing the missing link between these two fundamental results, and can be extended to an arbitrary odd number n of settings, an extension that can be seen as a particular violation of the n-cycle inequality.

Bell inequalities for the simplest exclusivity graph

Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest gra ...

Explicit form of correlation-function three-setting tight Bell inequalities for three qubits

We present a method to derive explicit forms of tight correlation-function Bell inequalities for three systems and dichotomic observables, which involve three settings for each observer. We also give sufficient and necessary conditions for quantum predictions to satisfy the new inequalities.

Experimental Tests of Classical and Quantum Dimensionality

We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semi-device-independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.

Bound entangled states with extremal properties

Following recent work of Beigi and Shor, we investigate positive partial transpose (PPT) states that are heavily entangled. We first exploit volumetric methods to show that in a randomly chosen direction, there are PPT states whose distance in trace norm from separable states is (asymptotically) at least 1/4. We then provide explicit examples of PPT states which are nearly as far from separable ones as possible. To obtain a distance of 2 - c from the separable states, we need a dimension of 2(poly[log(1/epsilon)]), as opposed to 2(poly(1/epsilon)) given by the construction of Beigi and Shor [J. Math. Phys. 51, 042202 (2010)]. We do so by exploiting the so-called private states, introduced earlier in the context of quantum cryptography. We also provide a lower bound for the distance between private states and PPT states and investigate the distance between pure states and the set of PPT states.