## Michał Dąbrowski

*University of Warsaw*

PhD student (since 2014) in the field of quantum optics and atomic physics at University of Warsaw, Poland. Since the 1st year of BSc studies he has been working in Quantum Memories Laboratory, group leaded by Prof. Wojciech Wasilewski. His research is mainly focus on generation of spatially multimode states of light, using both warm as well as cold atomic ensembles. He has been also involved in projects on micro-macro entanglement and EPR-steering generation between single photon and group of atoms. Currently during writing PhD thesis and looking for postdoc.

**Introduction** Entanglement is not only a central concept of the quantum theory, but also an essential resource in a variety of quantum-enhanced practical protocols. Particularly interesting is the broad concept of high-dimensional (HD) entangled states offering an unprecedented informational capacity that can be readily utilized in quantum key distribution (QKD). On the other hand, their generation and characterization requires a tremendous effort which highlights the need for other characterization techniques, e.g. based on compressive sensing or various witnesses.

**Methods** For bipartite HD entangled states the uncertainty relations have proven to be a viable way of detecting entanglement. In particular, the entropic steering inequalities are able to detect EPR-steering – a special case of entanglement related to the famous Einstein-Podolsky-Rosen (EPR) paradox. The generated state is EPR-steerable if the entropic witness Σ_{h}=h(x^{B}|x^{A})+h(k_{x}^{B}|k_{x}^{A}) is lower than log(πe), where h(x^{B}|x^{A}) and h(k_{x}^{B}|k_{x}^{A}) are conditional Shannon entropies for measurement in two conjugate, e.g. position and momentum bases. Another commonly used witness, well-suited to Gaussian states, is the product of variances: Π_{Δ2 }_{}_{}=<Δ^{2}(x^{B}|x^{A})><Δ^{2}(k_{x}^{B}|k_{x}^{A})>, which certifies EPR-steering if Π_{Δ2} < 1/4. Although, for a broad range of EPR-steerable states Σ_{h} confirms the EPR-steering while Π_{Δ2} might not.

**Results** We experimentally demonstrate generation and characterization of HD entangled and EPR-steerable state between single photon and macroscopic cold atomic ensemble, retrievable on demand using angularly-multimode quantum memory [1]. We certify the EPR-steering by measure true positions and momenta of Raman scattered photons using for the first time the single-photon resolving camera on the noisy data [2], without any background noise subtraction. Furthermore, we show that entropic witness vastly outperforms the variance-based witness. We highlighted and solved the difficulties in Shannon entropy estimation, characterizing the HD entangled state with highly undersampled data with different type of estimators.

**Discussion** The integration of the quantum memory presented here with a practical QKD scheme provides an instantaneous advantage as Bob (receiver) could perform measurements after Alice (sender) announces her basis thus effectively doubling the key rate generation. A quantum memory also opens new avenues to fundamental studies of one-particle uncertainty principles.

**References** [1] Nat. Commun. **8**, 2140 (2017); [2] arXiv: 1711.08948.

Quantum information processing and computing , Fundamental science for quantum technologies , Quantum optics and non-classical light sources