Demonstration of Einstein-Podolsky-Rosen Steering Using Hybrid Continuous- and Discrete-Variable Entanglement of Light
Adrien Cavaillès, Hanna Le Jeannic, Jérémy Raskop, Giovanni Guccione, Damian Markham, Eleni Diamanti, Matthew D. Shaw, Varun Boehm Verma, Sae Woo Nam, Julien Laurat
Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided device-independent quantum information protocols. Here we demonstrate steering using hybrid entanglement between continuous- and discrete-variable optical qubits. To this end, we report on suitable steering inequalities and detail the implementation and requirements for this demonstration. Steering is experimentally certified by observing a violation by more than 5 standard deviations. Our results illustrate the potential of optical hybrid entanglement for applications in heterogeneous quantum networks that would interconnect disparate physical platforms and encodings.
Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided device-independent quantum information protocols. Here we demonstrate steering using hybrid entanglement between continuous- and discrete-variable optical qubits. To this end, we report on suitable steering inequalities and detail the implementation and requirements for this demonstration. Steering is experimentally certified by observing a violation by more than 5 standard deviations. Our results illustrate the potential of optical hybrid entanglement for applications in heterogeneous quantum networks that would interconnect disparate physical platforms and encodings.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, refered as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, refered as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the two complementary encodings have emerged [1]. In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete and continuous-variable quantum states generated using optical parametric oscillators [2], located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Here we will report the first protocols based on this resource: the remote preparation of continuous-variable qubits [3], and a violation of an Einstein-Podolosky-Rosen steering inequality [4].
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
Summary form only given. Optical hybrid quantum information processing aims at mixing the traditionally separated discrete (DV) and continuous variable (CV) tools and concepts. In this approach, both DV states, such as single photons, and CV states, for example Schrödinger cats states: |cat ±〉 ∝ |α〉 ± | - α〉, are used. Having succeeded in experimentally generating hybrid entanglement of light for flying qubits [2], we will report on two protocols using this resource: the remote preparation of arbitrary CV qubits as well as the first demonstration of Einstein-Podolsky-Rosen (EPR) steering in the context of hybrid quantum information.
The first description of quantum steering goes back to Schrödinger.In 1935 he named it a necessary and indispensable feature of quantum mechanics in response to Einstein's concerns about the completeness of quantum theory.In recent years investigations of the effect have experienced a revival, as it turned out that steering is a distinct subclass of entanglement.It is strictly stronger than genuine entanglement, meaning that all steerable states are entangled but not vice versa, and strictly weaker than the violation of Bell inequalities.Additionally, the violation of a steering inequality has an intrinsic asymmetry due to the directional construction.One party seemingly steers the other and their roles are in general not interchangeable.The first direct observation of this asymmetry is presented in this thesis.It was demonstrated that certain Gaussian quantum optical states show steering from one party to the other but not in the opposite direction.This is a profound result, as the experiment proves that the class of steerable states itself divides into distinct subclasses.Furthermore, steering found major applications in quantum information.For example in the field of quantum key distribution (QKD) the non-classical correlations can be exploited to establish a secret, cryptographic key.Thereby, steering allows one-sided device independent security, since it violates a description with certain classical models.This thesis reports on the final results of the QKD project at the Leibniz University Hannover that aimed at the generation of a secure quantum key based on mutually entangled conjugate pairs of continuous variables.The protocol of a recent security proof was implemented in a table-top setup and nearly 100 MBit of usable key with composable and one-sided device independent security against coherent attacks were generated.The security analysis included finite size effects, and a newly developed hybrid reconciliation algorithm was used for efficient error correction.Furthermore, a loss study on the entanglement distribution showed that separation of the two detectors by a 5 km optical fibre would be possible.Therefore, the results of this work are a major step towards continuous variable QKD with state-of-the-art security in local area networks.
Shared quantum correlations find application in a wide range of modern quantum information protocols. This thesis presents several optical experiments towards the improved certification of shared quantum correlations, using photonic qubits. The first experiment demonstrates the Einstein–Podolsky–Rosen (EPR) steering effect with no detection loophole. Polarisation–entangled photon pairs generated in a Sagnac interferometer were used to test new loss–tolerant EPR steering inequalities. To test the robustness of the loss–tolerant EPR steering nequalities, a transmission loss of −4.3dB was introduced using a 1km optical fibre loop, finding inequality violations for n = 10 and n = 16 measurement settings with no detection loophole (equating to a total loss of 87%). The findings demonstrate how the new loss–tolerant protocols can be used to certify the EPR steering effect for arbitrarily high losses, and may find application in one–sided device–independent quantum key distribution protocols. The second experiment introduces EPR steering in the context of an EPR steering game. The rules of the game allow for certification of shared quantum correlations via EPR steering inequalites without requiring trust in devices or parties external to a quantum referee. In particular, the experiment successfully demonstrates EPR steering in a measurement–device independent framework; a framework which has typically been accessible only through Bell inequality violations. The findings suggest the possibility for quantum–refereed one–sided device–independent quantum key distribution protocols.
In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.