EPR-steering with angularly-multimode cold atoms quantum memory

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... [ view full abstract ]

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 =<Δ²(x^B|x^A)><Δ²(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.