Witnessing Trustworthy Single-Photon Entanglement with Local Homodyne Measurements

Abstract

Single-photon entangled states, i.e., states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped, and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one to say whether a given state is path entangled and also that entanglement lies in the subspace, where the optical paths are each filled with one photon at most, i.e., refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system. Our work provides a simple and trustworthy method for verifying the proper functioning of future quantum networks. Motivations.-Quantum networks [1] provide broad capabilities, ranging from long distance quantum communication at large scales [2,3], to the simulation of quantum many-body systems [4] in tabletop implementations. Remarkable progresses have been made in practice [5][6][7] and experimental capabilities are now advancing into a domain of rudimentary functionality for quantum nodes connected by quantum channels [8][9][10][11]. Surprisingly, the task of checking that a newly implemented quantum network performs well remains nontrivial.In the past decade, a great number of architectures based on atomic ensembles and linear optics have been proposed [12]. We now know that quantum networks based on singlephoton entanglement [13], i.e., entangled states of the form

Single-photon quantum nonlocality: Violation of the Clauser-Horne-Shimony-Holt inequality using feasible measurement setups

“…In the sign-binning case, (Z + = (−∞, 0]), the measurement operator reduces toX φ = 2/π(cos φσ x + sin φσ y ), and it is quite simple to see that there can be no violation of the CHSH inequality (this result was also found independently by some of us in Ref. [36]) because of the factor 2/π [37,38]. Our results indicate that a more general 'off-center' binning strategy does not change this result.…”

Proposed Entanglement of X-ray Nuclear Polaritons as a Potential Method for Probing Matter at the Subatomic Scale

“…Single-photon entanglement [39] refers to entanglement of two spatially distinguishable field modes by a single photon and lies at the heart of quantum networks [40,41]. In our setup, |1 − k |0 k is associated with registering the photon at the backward detector and |0 − k |1 k at the forward detector, in either case with no photon counts at the detector placed in the respective opposite direction.…”

Witnessing single-photon entanglement with local homodyne measurements: analytical bounds and robustness to losses

“…Here, we provide an extended analysis of this witness by introducing analytical bounds and by reporting measurements confirming its great robustness with regard to losses. This study highlights the potential of optical hybrid methods, where discrete entanglement is characterized through continuous-variable measurements.B where A and B are two spatial modes sharing a delocalized single-photon, has recently been proposed and experimentally tested [11]. It relies only on homodyne detections (i.e., on continuous quadrature measurements and not on photon counting) and offers significant advantages relative to other witnessing methods [12][13][14][15].…”

“…Also, in contrast with other entanglement witnesses [17], it specifically identifies the entanglement present in the singlephoton subspace. Finally, the measurements are only operated locally on the entangled modes, an important feature if applied to large-scale networks [18,19].The witness presented in [11] was built up on numerical arguments. In the present work, we extend its analysis by means of analytical calculations.…”

“…B where A and B are two spatial modes sharing a delocalized single-photon, has recently been proposed and experimentally tested [11]. It relies only on homodyne detections (i.e., on continuous quadrature measurements and not on photon counting) and offers significant advantages relative to other witnessing methods [12][13][14][15].…”