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International Conference on Transparent Optical Networks

Generation of energy-entangled W states

M. Menotti, Lorenzo Maccone, John E. Sipe, Marco Liscidini

Published Jul 1, 2017• 0 citations
Publisher

Abstract

Tripartite entangled states, such as Greenberger-Horne-Zeilinger (GHZ) and W states, are appealing for tests of fundamental aspects of quantum mechanics, as well as for implementations of quantum communication protocols. While the information is typically encoded in the polarization or path of the photons, we propose a feasible scheme to generate W states that are entangled in the energy degree of freedom. This is achieved by propagating photon pairs generated by parametric fluorescence in a linear optical circuit and post-selecting on the output channels. Such source can be easily integrated, profiting from high stability and a compact footprint. We also present a simple protocol to characterize the generated tripartite state, which is based on the reduced density matrix approach. Unexpectedly, although we rely on the energy degree of freedom, the full state tomography does not require any frequency conversion.

DOI
10.1109/icton.2017.8025174

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Tripartite entangled states, such as Greenberger-Horne-Zeilinger (GHZ) and W states, are appealing for tests of fundamental aspects of quantum mechanics, as well as for implementations of quantum communication protocols. While the information is typically encoded in the polarization or path of the photons, we propose a feasible scheme to generate W states that are entangled in the energy degree of freedom. This is achieved by propagating photon pairs generated by parametric fluorescence in a linear optical circuit and post-selecting on the output channels. Such source can be easily integrated, profiting from high stability and a compact footprint. We also present a simple protocol to characterize the generated tripartite state, which is based on the reduced density matrix approach. Unexpectedly, although we rely on the energy degree of freedom, the full state tomography does not require any frequency conversion.
Tripartite entangled states, such as Greenberger-Horne-Zeilinger and W states, are typically generated by manipulating two pairs of polarization-entangled photons in bulk optics. Here we propose a scheme to generate W states that are entangled in the energy degree of freedom in an integrated optical circuit. Our approach employs photon pairs generated by spontaneous four-wave mixing in a microring resonator. We also present a feasible procedure for demonstrating the generation of such a state, and we compare polarization-entangled and energy-entangled schemes for the preparation of W states.
The generation of multipartite entangled states is fundamental tool for a wide range of quantum information processing tasks, including teleportation, superdense coding, and quantum key distributions. This work demonstrates a scheme for high-fidelity Greenberger–Horne–Zeilinger (GHZ) and W states in a weakly coupled resonator- qubit-resonator system by exploiting quantum destructive interference and strategically suppresses higher-order transition pathways in the joint photonic Fock space to enable controlled and efficient tripartite entanglement.
The tripartite W state exhibits maximal entanglement between three parties, represented as 1/sqrt(3)(|001>+|010>+|100>), and has interesting applications for quantum communication, fundamental tests of quantum mechanics, and in quantum sensing and quantum computing. We experimentally demonstrate the generation of a three-photon discrete-energy-entangled W state in optical fiber. The source relies on multiphoton-pair generation via spontaneous four-wave mixing, and post-selection. By taking advantage of constraints imposed by the SFWM process, post-selection, and the properties of the W state, we verify the state produced by this source without resorting to frequency conversion.
We lay down a general scheme to quantify the amount of genuine tripartite entanglement present in the spatial and energy-time degrees of freedom of entangled photon triplets using a resource-based measure known as the tripartite entanglement of formation. Quantifying genuine tripartite entanglement relative to a number of maximally entangled three-qubit Greenberger-Horne-Zeilinger (GHZ) states called gebits, the tripartite entanglement of formation serves as a basis of comparison between different tripartite entangled states of differing dimension. Demonstrating genuine tripartite entanglement is doubly challenging because it is not enough to show that each party is inseparable from the other two (which is sufficient only for pure states). Instead, one must rule out all mixtures of all combinations of biseparable states from describing the tripartite state. To meet this challenge, we use entropic measures of the statistics of tripartite systems to simultaneously bound the correlations each party has with the other two, and in so doing place a lower limit to the tripartite entanglement of formation. Even though our measure never over-estimates the entanglement present, we estimate the effectiveness of our technique by determining the exact tripartite entanglement of a triple-gaussian triphoton wavefunction with the same correlations as seen in photon triplets generated in third-order spontaneous parametric down-conversion (SPDC). Between these two efforts, we show that a substantial amount of tripartite entanglement exists in both the spatial and energy-time degrees of freedom of these systems, and propose an experiment that can measure them.
Abstract An elementary tripartite quantum communication network for discrete variables is proposed. In this network three nodes are quantum wired with quantum channel created by a pair of Greenberger–Horne–Zeilinger (GHZ) triplet. We show that in this network by local operations and classical communication an arbitrary two-qubit state can be deterministically teleported from any node to any other node. In this network tripartite teleportation of two-qubit state is achieved by first splitting the qubit into fragments and then at the destination, qubit is re-constructed from the fragments. A high flux source for generation of fully inseparable GHZ photonic quantum channel required for developing an ideal tripartite quantum network is presented. This GHZ source employ a group velocity matched periodically poled potassium titanyl phosphate crystal in pulsed polarization Sagnac interferometer configuration and is based on selecting a three-photon entangled state from the product state of an entangled photon pair and a weak coherent state. This GHZ source generates tripartite entangled photons at telecom wavelength (1584 nm). Genuine entanglement in the generated GHZ state is detected with a witness ( W ) operator. Complete detail of the experimental apparatus required for developing an ideal tripartite quantum communication photonic network, which employ fully inseparable quantum channel, is presented. This quantum network fully operates at wavelength 1584 nm, which occurs in the L-band of the technologically important third telecom window. Success probability for teleportation of two-qubit photonic state within the tripartite quantum network is determined. We show that such quantum network is experimentally feasible. Experimental procedure to unambiguously verify the teleportation of an arbitrary two-qubit photonic state within the network is discussed. It is shown that our scheme can be implemented in a programmed teleportation system and it paves the way towards a large-scale quantum network.