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Generation of non-Gaussian quantum photonic states with multimode input resources

Mohamed Faouzi Melalkia, Juliette Huynh, Sébastien Tanzilli, Virginia D’Auria, Jean Etesse

Published Nov 3, 2021• 0 citations
OpenAlex

Abstract

Non-Gaussian quantum states of light are important resources for implementing quantum information tasks, ranging from fault-tolerant optical quantum information processing to long distance quantum communication. These states can be generated by applying non-Gaussian operations, such as photon addition and subtraction, to an input Gaussian quantum state. Also, the use of Gaussian operations (like homodyne measurement) allows the transformation of non-Gaussian input quantum states while maintaining their non-Gaussianity. It has been shown that in such context, iterative tailoring of arbitrary quantum states is possible, by cascading elementary operation blocks. This invitably comes at the cost of increasing the protocol complexity. Spectral modes, on the other hand, can be used to handily carry multiple quantum states in a single spatial mode. Moreover, multimode states populating such modes are readily available in commonly exploited processes such as spontaneous parametric down conversion.In this work, we propose a protocol to generate non-Gaussian quantum states using spectral multiplexing of input states and Gaussian operations. We give the analytical expression of the output non-Gaussian state as a function of the number of input state, the Gaussian operation and the properties of spectral modes carrying the input quantum states. Taking as an example the cat breeding operation, we show that with a single mixing and measurement operation, we can obtain an amplified output cat state comparable to the one obtained using iterative breeding scheme with multiple mixing operations and measurements with the same number of input states. We show also that the generation of approximated GKP states is possible with this protocol. We believe that the proposed protocol will have a major impact on the field of non-Gaussian quantum states generation, and can be used to extend the study beyond the cases considered in our work.

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Non-Gaussian quantum states of light are important resources for implementing quantum information tasks, ranging from fault-tolerant optical quantum information processing to long distance quantum communication. These states can be generated by applying non-Gaussian operations, such as photon addition and subtraction, to an input Gaussian quantum state. Also, the use of Gaussian operations (like homodyne measurement) allows the transformation of non-Gaussian input quantum states while maintaining their non-Gaussianity. It has been shown that in such context, iterative tailoring of arbitrary quantum states is possible, by cascading elementary operation blocks. This invitably comes at the cost of increasing the protocol complexity. Spectral modes, on the other hand, can be used to handily carry multiple quantum states in a single spatial mode. Moreover, multimode states populating such modes are readily available in commonly exploited processes such as spontaneous parametric down conversion.In this work, we propose a protocol to generate non-Gaussian quantum states using spectral multiplexing of input states and Gaussian operations. We give the analytical expression of the output non-Gaussian state as a function of the number of input state, the Gaussian operation and the properties of spectral modes carrying the input quantum states. Taking as an example the cat breeding operation, we show that with a single mixing and measurement operation, we can obtain an amplified output cat state comparable to the one obtained using iterative breeding scheme with multiple mixing operations and measurements with the same number of input states. We show also that the generation of approximated GKP states is possible with this protocol. We believe that the proposed protocol will have a major impact on the field of non-Gaussian quantum states generation, and can be used to extend the study beyond the cases considered in our work.
In this work, we study the generation of non-Gaussian quantum states of light using multimode quantum resources. We first propose a theoretical framework to describe photon subtraction operation - a well known non-Gaussian operation - applied to a multimode Gaussian state. We apply this framework to the case of Schrödinger kitten state generation using a multimode squeezed vacuum as input state. We show that a monomode non-Gaussian state with high purity can be generated by a better choice of the different experimental parameters. Then, we propose a new protocol to generate high amplitude non-Gaussian states using spectral multiplexing of input states and Gaussian operations. We show that this protocol can implement the cat breeding operation with less complexity. We show also that this protocol can be used for the generation of approximated GKP state.
Abstract Disposing of simple and efficient sources for photonic states with non-classical photon statistics is of paramount importance for implementing quantum computation and communication protocols. In this work, we propose an innovative approach that drastically simplifies the preparation of non-Gaussian states as compared to previous proposals, by taking advantage from the multiplexing capabilities offered by modern quantum photonics tools. Our proposal is inspired by iterative protocols, where multiple resources are combined one after the other for obtaining high-amplitude complex output states. Here, conversely, a large part of the protocol is performed in parallel, by using a single projective measurement along a mode which partially overlaps with all the input modes. We show that our protocol can be used to generate high-quality and high-amplitude Schrödinger cat states as well as more complex states such as error-correcting codes. Remarkably, our proposal can be implemented with experimentally available resources, highlighting its straightforward feasibility.
A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.
In the context of quantum technologies over continuous variables, Gaussian states and operations are typically regarded as freely available, as they are relatively easily accessible experimentally. In contrast, the generation of non-Gaussian states, as well as the implementation of non-Gaussian operations, pose significant challenges. This divide has motivated the introduction of resource theories of non-Gaussianity. As for any resource theory, it is of practical relevance to identify free conversion protocols between resources, namely, Gaussian conversion protocols between non-Gaussian states. Via systematic numerical investigations, we address the approximate conversion between experimentally relevant single-mode non-Gaussian states via arbitrary deterministic one-to-one mode Gaussian maps. First we show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit. Then we consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations. The numerical tools that we develop also allow one to devise conversions of trisqueezed into cubic-phase states beyond previously reported performances. Finally, we identify various other conversions which instead are not viable.
Hybrid bosonic codes combining bosonic codes with photon states offer a promising pathway for fault-tolerant quantum computation. However, the efficient generation of such states in optical setups remains technically challenging due to the requirement for complex non-Gaussian resources. In this paper, we propose a novel scheme to efficiently generate hybrid entangled states between a GKP qubit and a photon-number state using small-amplitude cat states as the primary resource. We apply a breeding process using small-amplitude cat states to increase the non-Gaussianity of the input states. This method requires only linear optical elements and homodyne measurements. Furthermore, we demonstrate that this protocol can be extended to generate hybrid qudit states. This scheme has the potential to provide a resource-efficient and experimentally attractive route toward implementing hybrid quantum error correction.
Non-Gaussian quantum states are crucial to fault-tolerant quantum computation with continuous-variable systems. Usually, generation of such states involves trade-offs between success probability and quality of the resultant state. For example, injecting squeezed light into a multimode interferometer and postselecting on certain patterns of photon-number outputs in all but one mode, a fundamentally probabilistic task, can herald the creation of cat states, Gottesman-Kitaev-Preskill (GKP) states, and more. We consider the addition of a non-Gaussian resource state, particularly single photons, to this configuration and show how it improves the qualities and generation probabilities of desired states. With only two modes, adding a single-photon source improves GKP-state fidelity from 0.68 to 0.95 and adding a second then increases the success probability eightfold; for cat states with a fixed target fidelity, the probability of success can be improved by factors of up to four by adding single-photon sources. These demonstrate the usefulness of additional commonplace non-Gaussian resources for generating desirable states of light.