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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Certification of Non-Gaussian States using Double Homodyne Detection

Ganaël Roeland, Ulysse Chabaud, Mattia Walschaers, Frédéric Grosshans, Valentina Parigi, Damian Markham, Nicolas Treps

Published Jun 21, 2021• 0 citations
Publisher

Abstract

Certifying reliable sources for quantum information processing is still one of the major challenges towards practical applications. Continuous variable quantum information provides a very promising platform where important resources such as scalable entanglement come "for free" [1] . In that context, a crucial quantum feature to look for and investigate is the so-called non-Gaussianity, which, beyond its conceptual relevance, is a necessary resource for any quantum computational advantage as well as for effective error correction, entanglement distillation and more. Non-Gaussian states have been produced and probed using full tomography techniques [2] . However, performing a full tomography of multimode continuous variable systems is a hard problem. Indeed, systems aimed at overcoming classical approach are by definition too complex to be fully characterized, thus alternative approaches are required.

DOI
10.1109/cleo/europe-eqec52157.2021.9542179

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Certifying reliable sources for quantum information processing is still one of the major challenges towards practical applications. Continuous variable quantum information provides a very promising platform where important resources such as scalable entanglement come "for free" [1] . In that context, a crucial quantum feature to look for and investigate is the so-called non-Gaussianity, which, beyond its conceptual relevance, is a necessary resource for any quantum computational advantage as well as for effective error correction, entanglement distillation and more. Non-Gaussian states have been produced and probed using full tomography techniques [2] . However, performing a full tomography of multimode continuous variable systems is a hard problem. Indeed, systems aimed at overcoming classical approach are by definition too complex to be fully characterized, thus alternative approaches are required.
Certifying reliable sources for quantum information processing is still one of the major challenges towards practical applications. Continuous variable quantum information provides a very promising platform where important resources such as scalable entanglement come “for free” [1]. In that context, a crucial quantum feature to look for and investigate is the so-called non-Gaussianity, which, beyond its conceptual relevance, is a necessary resource for any quantum computational advantage as well as for effective error correction, entanglement distillation and more. Non-Gaussian states have been produced and probed using full tomography techniques [2]. However, performing a full tomography of multimode continuous variable systems is a hard problem. Indeed, systems aimed at overcoming classical approach are by definition too complex to be fully characterized, thus alter-native approaches are required. In this work, we report on the use of double homodyne detection (see on Fig. 1(a)) on optical frequency comb pulses for the certification of non-Gaussian features of quantum states.
Entanglement is a key resource for many quantum applications. Understanding fundamental properties of entangled states is an important step towards their practical exploitation. We characterize entanglement in the context of Gaussian and non-Gaussian processes and identify entangled states that cannot be produced by any Gaussian evolution acting on separable states. This distinction exposes intrinsic limitations of Gaussian operations and highlights the role of non-Gaussian operations as an important resource. We apply this framework to develop a certification method that connects entanglement theory with quantum non-Gaussianity - an advanced quantum feature that is essential for several quantum applications. Our approach tailors the certification to experimentally relevant states that can be produced in current quantum optics experiments. We demonstrate this certification for recognizing the genuine non-Gaussian entanglement of various entangled Fock states and hybrid entangled states.
Quantum correlations are at the core of quantum information processing and are necessary to achieve a quantum computational advantage. In the context of continuous-variable quantum systems, another necessary resource for quantum advantages is non-Gaussianity. In this work, we propose a witness based on previously known relations between metrological power and quantum correlations, to detect a strong form of entanglement that only non-Gaussian states possess and that cannot be undone by passive optical operations, i.e., entanglement in all mode bases. The strength of our witness is two-fold: it only requires measurements in one basis to check entanglement in any arbitrary mode basis; it can be made applicable experimentally using homodyne measurements and without requiring a full tomography of the state.
The characterisation of quantum correlations, also known as entanglement, is central to quantum information theory. Operationally, entanglement gives rise to the notion of quantum non-locality, which challenges the ‘reality’ of quantum mechanics (adopting the terminology of Einstein, Podolski and Rosen) and arguably represents its most distinctive feature, in the sense that it calls for a departure from certain foundational tenets of classical physics. It should thus not come as a surprise that entanglement turns out to be a key resource for the implementation of a number of quantum communication protocols and also necessary to achieve computational speed-ups with quantum hardware, in the sense that accessing regions of the Hilbert space with entangled states allows one to shorten the computational depth of certain algorithms. Not surprisingly, generating and maintaining entanglement is generally difficult in practice, as it requires strong interactions between selected components of a system that must at the same time be isolated from the environment. Thanks to the techniques developed in quantum optical set-ups to achieve squeezed light, entanglement is, however, comparatively accessible with optical quantum continuous variables. As we shall see, in fact, continuous variable entanglement is closely related to the notion of squeezing. It is therefore of the utmost importance to be able to qualify and quantify the entanglement of quantum continuous variables, which is the subject matter of the present chapter. The first part of the chapter is devoted to techniques and criteria based on second moments to detect the entanglement of Gaussian states and also to the description of possible ways to quantify such quantum correlations, bearing in mind that the determination of entanglement monotones of clear operational significance is still an open problem, even in the restricted arena of Gaussian states. Although the criteria based on second moments are sufficient, but not necessary, for the detection of non-Gaussian entanglement too, we will push our analysis further by introducing more general criteria based on higher order statistical moments, which will be put to use to detect, on paper, the quantum correlations of an entangled cat-like state. We will also address the issues of entanglement distillation and quantum non-locality tests, in whose contexts we shall encounter other non-Gaussian operations and states, such as photon-subtracted states.
Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.
Quantum correlations are at the core of current developments in quantum technologies.Certification protocols of entanglement and steering, suitable for continuous-variable non-Gaussian states are scarce and generally highly demanding from an experimental point of view.We propose a protocol based on Fisher information for witnessing steering in general continuous-variable bipartite states, through homodyne detection.It proves to be relevant for the detection of non-Gaussian steering in scenarios where witnesses based on Gaussian features like the covariance matrix are shown to fail.