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Optical quantum state engineering with multimode resources: between a drawback to be circumvented and an advantage to be exploited

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

Published May 31, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.2621373

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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.
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.
Optical non-Gaussian quantum states can be generated in a heralded manner by applying a photon subtraction operation to a Gaussian input state. In our work, we develop a theoretical framework to describe this operation in the case where the input state is spectrally multimode. This framework allows the optimal design of photon subtraction experiments. We give the exact expression of the generated non-Gaussian state in the general case. We apply this framework to the case of Schrodinger kitten state generation using a multimode squeezed vacuum as input state. We show that the quality of the generated state (in terms of fidelity and Wigner function negativity) can be enhanced by adapting the different experimental parameters.
This paper establishes a versatile theoretical framework that explicitly describes single-photon subtraction from multimode quantum light in the context of non-Gaussian state generation and manipulation. The treatment focuses on easy-to-implement configurations in which no mode-selective operation is available and evaluates features and advantages of schemes where only simple filtering stages are employed on the experiments. Such configuration, by considerably reducing the experimental overheads, makes experiments involving single-photon subtraction easier to be implemented. The obtained theoretical framework allows retrieving, given a multimode input state, optimal conditions required to herald and then to detect non-Gaussian states, providing a practical and powerful toolbox for experiments' design. The application of the proposed approach to the case study of Schr\"odinger cat state preparation starting from a frequency multimode squeezed state illustrates the impact of the derived theoretical tools.
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.
We propose a high-rate generation method of optical Schr\"odinger cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\ensuremath{\alpha}|\ensuremath{\ge}2)$ can exceed megacounts per second, about 103{10}^{3}103 to 106{10}^{6}106 times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. The ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalability has been demonstrated but preparation of non-Gaussian states of light remains as a challenging task for universality and fault tolerance. Our proposal reduces the difficulty of the state preparation and opens a way for practical applications in quantum optics.