Modular variables in quantum theory : final report

We experimentally detect entanglement in modular position and momentum variables of photon pairs which have passed through $D$ -slit apertures. We first employ an entanglement criteria recently proposed in [Phys. Rev. Lett. 106, 210501 (2011)], using variances of the modular variables. We then propose an entanglement witness for modular variables based on the Shannon entropy and test it experimentally. Finally, we derive criteria for Einstein-Podolsky-Rosen-steering correlations using variances and entropy functions. In both cases, the entropic criteria are more successful at identifying quantum correlations in our data.We experimentally detect entanglement in modular position and momentum variables of photon pairs which have passed through $D$-slit apertures. We first employ an entanglement criteria recently proposed in [Phys. Rev. Lett. 106, 210501 (2011)], using variances of the modular variables. We then propose an entanglement witness for modular variables based on the Shannon entropy and test it experimentally. Finally, we derive criteria for Einstein-Podolsky-Rosen-steering correlations using variances and entropy functions. In both cases, the entropic criteria are more successful at identifying quantum correlations in our data.

arXiv:1208.6222Physical Review ASep 24, 201244 citations

Perspectives in quantum theory

Wolfgang Yourgrau, Alwyn van der Merwe, Alfred Landé

Dover Publications eBooksJan 1, 1971247 citations

Quantum information processing in phase space: A modular variables approach

Andreas Ketterer, Arne Keller, Stephen Patrick Walborn +2 more

Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.

arXiv:1512.02957Physical Review AAug 22, 201643 citations

Elements of Quantum Theory

William T. Dixon

Springer eBooksJan 1, 19720 citations

Quantum Mathematics II

Michele Correggi, Marco Falconi

Springer INdAM seriesJan 1, 20234 citations

We experimentally detect entanglement in modular position and momentum variables of photon pairs which have passed through

D

-slit apertures. We first employ an entanglement criteria recently proposed in [Phys. Rev. Lett. 106, 210501 (2011)], using variances of the modular variables. We then propose an entanglement witness for modular variables based on the Shannon entropy and test it experimentally. Finally, we derive criteria for Einstein-Podolsky-Rosen-steering correlations using variances and entropy functions. In both cases, the entropic criteria are more successful at identifying quantum correlations in our data.