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Programmable Multimode Quantum Networks
Seiji Armstrong, Jean-Francois Morizur, Jiri Janousek, Boris Hage, Nicolas Treps, Ping Koy Lam, Hans-A. Bachor
TL;DR
The paper addresses the complexity and limited flexibility of conventional optical networks for generating multimode entanglement. It emulates switchable linear-optics networks through software-controlled spatial-mode combinations, demonstrating entanglement from N=2 to N=8 and scalability through additional detector photodiodes.
Problem
Conventional multimode-entanglement generation requires complex beam-splitter and phase-shifter layouts that need substantial modification for each new set of entangled modes.
Method
The approach emulates linear-optics networks by software-controlled combinations of copropagating spatial modes measured with multi-pixel detectors.
Results
N=2 through N=8 multimode entanglement was demonstrated, with measured correlations satisfying inseparability criteria and scalability simulated to 30 modes.
Takeaways & Limitations
The scheme provides flexible, efficient multimode-entanglement generation in which larger non-cluster mode bases require more detector photodiodes without modifying the optical setup.
Takeaways & Limitations
Complex one-way measurement-based computations additionally require arbitrary homodyne angles for each mode and feed-forward to any desired mode.
Abstract
from arXiv · showhide
Entanglement between large numbers of quantum modes is the quintessential resource for future technologies such as the quantum internet. Conventionally the generation of multimode entanglement in optics requires complex layouts of beam-splitters and phase shifters in order to transform the input modes in to entangled modes. These networks need substantial modification for every new set of entangled modes to be generated. Here we report on the highly versatile and efficient generation of various multimode entangled states with the ability to switch between different linear optics networks in real time. By defining our modes to be combinations of different spatial regions of one beam, we may use just one pair of multi-pixel detectors each with M photodiodes in order to measure N entangled modes, with a maximum number of N=M modes. We program virtual networks that are fully equivalent to the physical linear optics networks they are emulating. We present results for N=2 up to N=8 entangled modes here, including N=2,3,4 cluster states. Our approach introduces flexibility and scalability to multimode entanglement, two important attributes that are highly sought after in state of the art devices.
Discussion
The paper verifies multimode entanglement using van Loock–Furusawa inseparability criteria, requiring N−1 inequalities for an N-mode state.
- Discussion: N−1 inseparability inequalities are sufficient to verify entanglement in an N-mode state.The criteria are applied to measured mode bases.
(I)
The programmable spatial-mode scheme demonstrates entanglement across up to eight modes and supports real-time switching among several entangled-state networks. Its scalability is bounded by detector resources and, for cluster states, by the number of squeezed inputs and access to additional measurement capabilities.
- (I): For N-mode states, the experiment evaluates N−1 inseparability inequalities using optimized homodyne gains.For unweighted cluster states, all homodyne gains are set to 1.
- (I): Correlations remain in the quantum regime up to 30 simulated modes, although inseparability approaches the classical bound as unsqueezed inputs add vacuum noise.The measured setup is limited to eight modes, and theoretical predictions agree with experimental values without transformation loss.
- (I): Larger non-cluster entangled-mode bases require more photodiodes but no optical-setup modification, whereas cluster states require additional squeezed inputs.The number of measurable modes is increased through the MPHD detector array.
- (I): 0.58 ± 0.01: measured optimal EPR entanglement for N=2, with an optimized beam-splitter ratio of 48.8%.The asymmetric input squeezing levels make 48.8% slightly better than a symmetric 50% network.
- (I): The setup enables protocols such as quantum teleportation, but one-way measurement-based computation requires arbitrary homodyne angles and feed-forward to any desired mode.The paper states that both capabilities are feasible with existing technologies.
Methods
The method constructs virtual linear-optics networks from spatial-mode measurements, using programmable gains and beam-splitter transformations to generate and verify multimode and cluster-state bases.
- Experimental setup: The experiment uses a dual-wavelength laser, optical parametric amplifiers, an eight-photodiode array, and 80% quantum-efficiency photodiodes to measure spatial modes.The array contains 16 photodiodes, but eight are used; its 90% filling factor leaves 10% of light inactive.
- Virtual Networks: For even N, two squeezed modes are combined on a half-reflecting beamsplitter and then symmetrically mixed with N−2 vacuum modes.This construction applies to N = 2, 4, 6, and 8 mode bases.
- Virtual Networks: Odd-N networks modify the EBS reflectivity, add phase shifts, swap selected outputs, and optimize homodyne gains using a genetic algorithm.The gains are optimized to maximize satisfaction of the van Loock–Furusawa inequalities while minimizing their mean.
- Spatial mode bases: Each row of Uin specifies electronic gains that recover an input spatial mode, including the Gaussian and phase-flipped Gaussian modes.Setting Unet = I labels the rows of Uin as the input modes.
- Network programming: The input modes are mixed by Unet, an N × N matrix representing the concatenated beam-splitters and phase shifts of the emulated linear-optics network.The accessible phase shifts are π shifts, equivalent to multiplying a mode by −1.
- Cluster-state verification: Cluster-state inseparability is assessed with van Loock–Furusawa criteria for N = 3, 4, and 5 mode configurations.The criteria require the listed sums of quadrature variances to remain below 1.
Competing financial interests
The paper uses virtual linear-optics networks and spatial-mode measurements to characterize multimode entanglement across several mode bases.
- Virtual networks map squeezed inputs and vacua onto entangled mode bases using beam-splitter and phase-shift operations.
- The setup measures spatial-mode quadratures with multi-pixel homodyne detection and programmable electronic gain functions.
- Measured noise variances and correlations assess inseparability across multimode bases, including symmetric pairwise entanglement.
- The figure compares ordinary multimode entanglement with cluster-state inseparability against a separability bound and theoretical predictions.